# Arithmetic Aptitude :: Permutation and Combination

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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.

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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.

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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

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In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A63

B90

C126

D45

E135

Explanation:

Total 7 men and 3 women

5 men can be selected from 7 men in 7C5 ways

2 women can be selected from 3 women in 3C2 ways

So 7C5*3C2= 63 ways.

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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.

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How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

A40

B400

C5040

D2520

Explanation:

LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.

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23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.

A23

B20

C22

D1

ENone of these

Explanation:

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Six friends go to pizza corner there are 2 types of pizzas. And six different flavors are there they have to select 2 flavors from 6 flavors. In how many ways we can select?

A6C2

B6P2

C(6C2)/2!

DNone of these

Explanation:

Number of ways 2 flavors can be selected out of 6 flavors = 6c2 = 15

Number of ways pizza can be selected = 2 [there are 2 types of pizzas]

âˆ´ Number of ways to select a pizza = 2 Ã— 15 = 30 ways

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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:

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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

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