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Q:

In How many ways is it possible to make a selection by taking any number of 15 fruits, namely 3 oranges, 5 apples and 7 mangoes?

A) 131	B) 191
C) 68	D) 3720

Answer & Explanation Answer: B) 191

Explanation:

Out of 15 fruits, 7 are alike of one kind, 5 are alike of a second kind and 3 are alike of a third kind.

Hence, the required number of ways = [ (7+1) (5+1) (3+1) -1] =191

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Filed Under: Permutations and Combinations

Q:

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123	B) 113
C) 246	D) 945

Answer & Explanation Answer: C) 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.

(i) 1 lady out of 4 and 4 gentlemen out of 6

(ii) 2 ladies out of 4 and 3 gentlemen out of 6

(iii) 3 ladies out of 4 and 2 gentlemen out of 6

(iv) 4 ladies out of 4 and 1 gentlemen out of 6

In case I the number of ways = $C_{1}^{4} \times C_{4}^{6}$ = 4 x 15 = 60

In case II the number of ways = $C_{2}^{4} \times C_{3}^{6}$ = 6 x 20 = 120

In case III the number of ways = $C_{3}^{4} \times C_{2}^{6}$ = 4 x 15 = 60

In case IV the number of ways = $C_{4}^{4} \times C_{1}^{6}$ = 1 x 6 = 6

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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Filed Under: Permutations and Combinations
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

Q:

In how many ways can 5 letters be posted in 4 letter boxes?

A) 512	B) 1024
C) 625	D) 20

Answer & Explanation Answer: B) 1024

Explanation:

First letter can be posted in 4 letter boxes in 4 ways. Similarly second letter can be posted in 4 letter boxes in 4 ways and so on.

Hence all the 5 letters can be posted in = 4 x 4 x 4 x 4 x 4 = 1024

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Q:

5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?

A) 2880	B) 1440
C) 720	D) 2020

Answer & Explanation Answer: A) 2880

Explanation:

There are total 9 places out of which 4 are even and rest 5 places are odd.

4 women can be arranged at 4 even places in 4! ways.

and 5 men can be placed in remaining 5 places in 5! ways.

Hence, the required number of permutations = 4! x 5! = 24 x 120 = 2880

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Filed Under: Permutations and Combinations
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

Q:

Arrange the given words in a meaningful sequence.

1. Adult 2. Child 3. Infant 4. Boy 5. Adolescent

A) 1, 3, 4, 5, 2	B) 2, 3, 5, 4, 1
C) 2, 3, 4, 1, 5	D) 3, 2, 4, 5, 1

Answer & Explanation Answer: D) 3, 2, 4, 5, 1

Explanation:

The Correct Sequence is:

Infant Child Boy Adolescent Adult

3 2 4 5 1

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Filed Under: Logical Sequence of Words

Q:

Arrange the given words in a meaningful sequence.

1. Rainbow 2. Rain 3. Sun 4. Happy 5. Child

A) 4, 2, 3, 5, 1	B) 2, 3, 1, 5, 4
C) 4, 5, 1, 2, 3	D) 2, 1, 4, 5, 3

Answer & Explanation Answer: B) 2, 3, 1, 5, 4

Explanation:

The Correct Sequence is:

Rain Sun Rainbow Child Happy

2 3 1 5 4

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Filed Under: Logical Sequence of Words

Q:

Arrange the given words in a meaningful sequence.

1. Ceiling 2. Room 3. Floor 4. Walls 5. Foundation

A) 5,4,1,3,2	B) 5,4,3,1,2
C) 4,5,3,1,2	D) 4,5,1,2,3

Answer & Explanation Answer: A) 5,4,1,3,2

Explanation:

The Correct Sequence is:

Foundation Walls Ceiling Floor Room

5 4 1 3 2

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Filed Under: Logical Sequence of Words

Q:

Arrange the given words in a meaningful sequence.

1. Flat 2. Home 3. Building 4. Society 5. Place

A) 5,4,3,1,2	B) 5,4,3,2,1
C) 4,3,1,2,5	D) 4,5,3,1,2

Answer & Explanation Answer: A) 5,4,3,1,2

Explanation:

The Correct Sequence is :

Place Society Building Flat Home

5 4 3 1 2

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Filed Under: Logical Sequence of Words

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