Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 25

EASY

JEE Main/Advance

IMPORTANT

Earn 100

Find number of ways of distributing $8$ different items equally among two children.

Important Questions on Permutation and Combination

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 26

(a) In how many ways can five people be divided into three groups?
(b) In how many ways can five people be distributed in three different rooms if no room must be empty?
(c) In how many ways can five people be arranged in three different rooms if no room must be empty and each room has

5

seats in a single row.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 27

Prove that

: \frac{200!}{(10!)^{20} \cdot 19!}

is an integer

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 28

In how many ways

5

persons can sit at a round table, if two of the persons do not sit together?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 29

In how many ways four men and three women may sit around a round table if all the women are together?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 30

Seven persons including

A, B, C

are seated on a circular table. How many arrangements are possible if

B

is always between

A

and

C

?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 31

In how many ways four

' +'

and five

' -'

sign can be arranged in a circles so that no two

' +'

sign are together.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 32

Let $N = 24500$ , then find

(i) The number of ways by which $N$ can be resolved into two factors.

(ii) The number of ways by which $5 N$ can be resolved into two factors.

(iii) The number of ways by which $N$ can be resolved into two co-prime factors.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 33

Find the number of ways of selection of one or more letters from $AAAABBCCCDEF$

(i) there is no restriction.

(ii) the letters $A & B$ are selected atleast once.

(iii) only one letter is selected.

(iv) atleast two letters are selected