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Permutation and Combination Questions

NA
SHSTTON
88
Solv. Corr.
57
Solv. In. Corr.
145
Attempted
0 M:31 S
Avg. Time

1 / 100

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
78
Solv. Corr.
66
Solv. In. Corr.
144
Attempted
2 M:23 S
Avg. Time

2 / 100

Choose the correct option.

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
25
Solv. Corr.
113
Solv. In. Corr.
138
Attempted
0 M:39 S
Avg. Time

3 / 100

Choose the correct option.

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

NA
SHSTTON
172
Solv. Corr.
212
Solv. In. Corr.
384
Attempted
0 M:25 S
Avg. Time

4 / 100

Choose the correct option.

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.

Workspace

NA
SHSTTON
136
Solv. Corr.
159
Solv. In. Corr.
295
Attempted
1 M:54 S
Avg. Time

5 / 100

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
162
Solv. Corr.
73
Solv. In. Corr.
235
Attempted
1 M:57 S
Avg. Time

6 / 100

Choose the correct option.

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.

Workspace

NA
SHSTTON
70
Solv. Corr.
101
Solv. In. Corr.
171
Attempted
0 M:38 S
Avg. Time

7 / 100

Choose the correct option.

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:

Workspace

NA
SHSTTON
109
Solv. Corr.
160
Solv. In. Corr.
269
Attempted
0 M:31 S
Avg. Time

8 / 100

Choose the correct option.

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

Workspace

NA
SHSTTON
57
Solv. Corr.
92
Solv. In. Corr.
149
Attempted
0 M:58 S
Avg. Time

9 / 100

Choose the correct option.

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
105
Solv. Corr.
182
Solv. In. Corr.
287
Attempted
1 M:22 S
Avg. Time

10 / 100

Choose the correct option.

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

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