Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 9

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If the numbers of circular arrangements of $50$ persons including $A$ and $B$ such that there are exactly $24$ persons between $A$ and $B$ and there are $12$ persons between $A$ and $B$ are $m$ and $n$ respectively, then $\frac{m}{n}$ is

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Important Questions on Permutations and Combinations

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 10

Number of

5

digit numbers which have exactly three

5' s

is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 11

Number of total numbers divisible by

3

and lying between

100

and

1000

using the digits

0, 1, 2, 3, 4

if the repetition of digits is not allowed, is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 12

Number of outcomes, when

3

identical dice are thrown together, is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 13

A class has

15

students. The number of ways of forming a team of students including at least two students and also excluding at least two students, is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 14

Five balls are to be placed in four boxes. Each can hold all the five balls. Number of ways in which we can place the balls so that no box remains empty, if the balls as well as boxes are identical, is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 15

The total number of

5

-digit numbers of different digits using the digits

0, 1, 2, . . . . . . . 7

, in which the digit in the middle is the largest is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 16

If

\sum_{k = 0}^{n} (k^{2} + k + 1) k! = (2007) \cdot 2007!

, then value of

n

is

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 1

If

{}^{n}C_{4}, {}^{n}C_{5}

and

{}^{n}C_{6}

are in

A . P .

, then value of

n

can be :