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# Permutation and Combination Questions

NA
SHSTTON
59
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Solv. In. Corr.
90
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Choose the correct option.

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

A360

B480

C720

D5040

Explanation:

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

Workspace

NA
SHSTTON
44
Solv. Corr.
40
Solv. In. Corr.
84
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1 M:24 S
Avg. Time

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6 people A,B,C,D,E and F sit around a table for dinner. Since A does not like C, he doesn't sit either opposite or beside C.B and F always like to sit opposite each other.
If A is beside F then who is are the two neighbours of B?

AE and C

BD and C

CD and E

DEither (a) or (b)

Explanation:

As shown in this diagram , D and E are two neighbours of B.

Workspace

NA
SHSTTON
12
Solv. Corr.
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Solv. In. Corr.
75
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6 people A,B,C,D,E and F sit around a table for dinner. Since A does not like C, he doesn't sit either opposite or beside C.B and F always like to sit opposite each other.
If D is adjacent to F then who is adjacent to C?

AE and B

BD and A

CD and B

Deither (a) or (c)

Explanation:

Here is no explanation for this answer

Workspace

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SHSTTON
85
Solv. Corr.
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Solv. In. Corr.
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1 M:11 S
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Choose the correct option.

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

A810

B1440

C2880

D50400

Explanation:

In the word "CORPORATION",treat those vowels OOAIO as one letter.

so it will be "CRPRTN (OOAIO)".

which is having 7 (6 + 1) letters. out of which R occurs 2 times and the rest are different.

Number of ways arranging these letters = (7!/2!) = 2520.

Now 5 vowels in which O occurs 3 times and the rest are different, can be arranged as 5!/3! = 20 ways.

So required number of ways = (2520 x 20) = 50400.

Workspace

NA
SHSTTON
34
Solv. Corr.
66
Solv. In. Corr.
100
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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

A12

B11

C13

D18

Explanation:

Workspace

NA
SHSTTON
75
Solv. Corr.
126
Solv. In. Corr.
201
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1 M:22 S
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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

A564

B645

C735

D756

Explanation:

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

Required number of ways = (7C3 * 6C2)+(7C4 * 6C1)+(7C5)
=>[(7*6*5)/(3*2*1) * (6*5)/(2*1)]+(7C3 * 6C1) + (7C2)

=> 525 + [(7*6*5)/(3*2*1)* 6]+[(7*6)/(2*1)]

= (525 + 210 + 21)
= 756

Workspace

NA
SHSTTON
103
Solv. Corr.
105
Solv. In. Corr.
208
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Choose the correct option.

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

A10080

B4989600

C120960

DNone of these

Explanation:

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

So,Number of ways of arranging these letters = (8!/2!*2!)=10080.

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters = (4!/2)=12.
=> Required number of words = (10080 * 12) = 120960.

Workspace

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SHSTTON
55
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60
Solv. In. Corr.
115
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8 / 12

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In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together

A2880

B1440

C5760

DNone of these

Explanation:

The lions and the tigers can be arranged in 5!*4!= 2880 ways

Workspace

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SHSTTON
21
Solv. Corr.
60
Solv. In. Corr.
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When all words in "MASTER" is sorted in alphabetical order then what is the 49th word ?

AA R E M S T

BA E R M S T

CA M E R S T

DNone of these

Explanation:

Arranged alphabet: A E M R S T
next, A E _ _ _ _=24
next, A M _ _ _ _=24
total word is 48
so.word at 49 rank is A R E M S T.

Workspace

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25
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Choose the correct option.

LEADING" arrange it in such a way that atleast two vowels always together ?

A3600

B2160

C5040

D720

Explanation:

Total possible arrangement = 7! = 5040

Given condition 2 vowel should comes together : {_L_D_N_G_)

So, 3 vowels can be placed at 5 positions = 5p3 * 4! = 60*24 = 1440.

So required arrangements : (5040 - 1440) = 3600

Workspace

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