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Permutation and Combination

If there are 5 routes for travelling two places A and B. How many option are there for a a person to travel from A to B and return back[2015]

5

10

9

25

A school committee consists of 2 teachers and 4 students, the number of diffrent committees that can be formed from 5 teachers and 10 students are [2014]

8

10

15

2100

Out of 7 consonants and 4 words. How many word of 3 cononants and 2 vowels can be formed[2013]

25200

210

1400

1050

Find the arrangement that can be made out of the letters of the word 'MANAGEMENT'[2009]

453600

456300

45300

226800

In how many ways four persons. A, B, C, D can be arranged taking 2 person at a time[2008]

12

15

16

18

Other Questions

How many three letter words are formed using the letters of the word TIME?

12

20

16

24

Solutions

4P3 = 4 x 3 x 2 = 24

Using all the letters of the word "THURSDAY", how many different words can be formed?

8

8!

7

7!

Solutions

Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.

The number of different permutations of the word BANANA is

720

60

120

360

Solutions

Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?

3

6

24

120

Solutions

The number of words = 3! = 6.

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

32

48

36

60

Solutions

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

120

720

4320

2160

Solutions

The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.

A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?

165

185

205

225

Solutions

Total number of persons in the committee = 5 + 6 = 11
11C8 = 165

In how many ways can six members be selected from a group of ten members?

8C4

10C4

10C5

10P4

Solutions

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?

63

90

126

45

Solutions

If nPr = 3024 and nCr = 126 then find n and r.

9, 4

10, 3

12, 4

11, 4

Solutions

Explanation: nPrnCr=3024126$\frac{^nP_r}{^nC_r} = \frac{3024}{126}$
nPr=n!(nr)!$^nP_r = \frac{n!}{(n-r)!}$
nCr=n!(nr)!×r!$^nC_r = \frac{n!}{(n-r)!×r!}$
Hence [n!(nr)!]÷[n!(nr)!×r!]$[\frac{n!}{(n-r)!}]÷[\frac{n!}{(n-r)!×r!}]$ = 24
24 = r!
Hence r = 4
Now nP4 = 3024
n!(n4)!=3024$\frac{n!}{(n-4)!} = 3024$
n(n-1)(n-2)(n-3) = 9.8.7.6
n = 9.

If 10Pr = 720, then r is equal to

4

2

3

1

Number of ways in which 12 different ball can be divided into group of 5,4 and 3 balls are.

12! / 5! 4!

12! / 5! 4! 3!

12! / 5! 4! 3! 3!

None of these

In how many ways can a committee of 5 made out 6 men and 4 women containing at least one women?

246

222

186

None of these

Solutions

A committee of 5 out of 6 + 4 - 10 can be made in 10C5 = 252 ways
If no woman is to be included, then number of ways = 5C5 = 6
the required number = 252 - 6 = 246

If nPr = 720 nCr then r is equal to

3

7

6

4

Solutions

n! / (n - r)! = 720(n!) / (n - r)!r!
r! = 720
r = 6

How many new work are possible from the letter of the word PERMUTATION?

11! / 2!

(11! / 2!) - 1

11! - 1

None of these

I there is