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If $n$ identical dice are rolled, then number of possible out comes are

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Important Questions on Permutation and Combination

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 13

Number of ways in which a pack of

52

playing cards be distributed equally 'among four players so that each have the Ace, King, Queen and Jack of the same suit, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 14

Find the total number of positive integral solutions of

15 < x_{1} + x_{2} + x_{3} \leq 20

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 15

Seven persons

P_{1}, P_{2}, \dots \dots \dots, P_{7}

initially seated at chairs

C_{1}, C_{2} \dots \dots \dots, C_{7}

, respectively. They all left there chairs simultaneously for hand wash. Now in how many ways they can again take seats such that no one sits on his own seat and

P_{1}

sits on

C_{2}

and

P_{2}

sits on

C_{3} ?

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 16

Given six line segments of length

2, 3, 4, 5, 6, 7

units, the number of triangles that can be formed by these segments is

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 17

There are

m

apples and

n

oranges to be placed in a line such that the two extreme fruits being both oranges. Let

P

denotes the number of arrangements if the fruits of the same species are different and

Q

the corresponding figure when the fruits of the same species are alike, then the ratio of

P : Q

has the value equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 18

The number of intersection points of diagonals of

2009

sides regular polygon, which lie inside the polygon.

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 19

A rectangle with sides $2 m - 1$ and $2 n - 1$ is divided into squares of unit length by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is

Question Image

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 20

Find the number of all rational numbers $\frac{m}{n}$ such that:

(i) $0 < \frac{m}{n} < 1$

(ii) $m$ and $n$ are relatively prime

(iii) $m \cdot n = 25!$

If n identical dice are rolled, then number of possible out comes are

Important Questions on Permutation and Combination

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If $n$ identical dice are rolled, then number of possible out comes are