Permutations and Combinations Questions

MathematicsPermutations and Combinations57 Questions Found

MathematicsCombinations and SelectionJEE Advanced 1981Moderate

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Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty ?

Answer:300

MathematicsCombinations and SelectionJEE Advanced 1984Easy

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The side $A B, B C$ and $C A$ of a triangle $A B C$ have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is .........

Answer:205

MathematicsCombinations and SelectionJEE Advanced 1985Moderate

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7 relatives of a man comprises 4 ladies and 3 gentlemen; his wife has also 7 relatives; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?

Answer:485

MathematicsCombinations and SelectionJEE Advanced 1986Easy

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A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

Answer:64

MathematicsLinear PermutationsJEE Advanced 1988Easy

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Total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs occur together is .........

Answer:35

MathematicsCombinations and SelectionJEE Advanced 2014Easy

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Let $n_{1} < n_{2} < n_{3} < n_{4} < n_{5}$ be positive integers such that $n_{1} + n_{2} + n_{3} + n_{4} + n_{5} = 20$ . Then the number of such distinct arrangements $(n_{1}, n_{2}, n_{3}, n_{4}, n_{5})$ is

Answer:7

MathematicsLinear PermutationsJEE Advanced 2015Moderate

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Let $n$ be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

Answer:5

MathematicsCombinations and SelectionJEE Advanced 1979Easy

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$^{n} C_{r - 1} = 36,^{n} C_{r} = 84$ and $^{n} C_{r + 1} = 126$ , then $r$ is:

(A)

(B)

(C)

(D)

None of these.

Answer:C

MathematicsLinear PermutationsJEE Advanced 1982Easy

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Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

(A)

^{6} C_{3} \times^{4} C_{2}

(B)

^{4} P_{2} \times^{6} P_{3}

(C)

^{4} C_{2} +^{4} P_{3}

(D)

none of these

Answer:B

MathematicsFundamental Principle of CountingJEE Advanced 1982Easy

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Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are

(A)

69760

(B)

30240

(C)

99748

(D)

none of these

Answer:A

...6

Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty ?

7 relatives of a man comprises 4 ladies and 3 gentlemen; his wife has also 7 relatives; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

Total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs occur together is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } nCr−1​=36,nCr​=84 and nCr+1​=126, then r is:

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are

Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty ?

7 relatives of a man comprises 4 ladies and 3 gentlemen; his wife has also 7 relatives; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

Total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs occur together is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } nCr−1​=36,nCr​=84 and nCr+1​=126, then r is:

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are

$^{n} C_{r - 1} = 36,^{n} C_{r} = 84$ and $^{n} C_{r + 1} = 126$ , then $r$ is:

$^{n} C_{r - 1} = 36,^{n} C_{r} = 84$ and $^{n} C_{r + 1} = 126$ , then $r$ is: