RRB NTPC - Permutations Combinations

1.

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

   A.) 260
   B.) 240
   C.) 120
   D.) None of these

Answer: Option 'C'

'SCHOOL' contains 6 different letters.
vowels OO are always together 
we have to arrange the letters (OO)SCHL 
Now 5 letters can be arranged in 5! = 120 ways 
The vowels (OO) can be arranged 2! = 2 ways.
= (120 x 2) = 240 
again you have to divided 2 common vowels so answer is 120.

2.

If all the numbers 2, 3, 4, 5, 6, 7, 8 are arranged, find the number of arrangements in which 2, 3, 4, are together? 

   A.) 720
   B.) 620
   C.) 700
   D.) None of these

Answer: Option 'A'

Answer: Option 'A'
If (2 3 4) is one. 
we must arrange (2 3 4), 5, 6, 7, 8 in 
5P5 = 5! = 120 ways 
2, 3, 4 can be arranged in 3P3 = 3! = 6 
120 × 6 = 720.

3.

In how many different number of ways a combination of 3 persons can be selected from 4 men and 2 women.

   A.) 150
   B.) 200
   C.) 250
   D.) None of these

Answer: Option 'B'

6C3 × 5C2
6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
5C2
= 5!/(3! . 2!)
= 5 × 2 = 10
= 20 × 10 = 200.

4.

Find 10P6 

   A.) 150200
   B.) 151200
   C.) 152200
   D.) None of these

Answer: Option ''

Answer: Option 'B'
10P6 = 10!/4! = 10 × 9 × 8 × 7 × 6 × 5 
= 151200.

5.

In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons? 

   A.) 230
   B.) 203
   C.) 220
   D.) 210

Answer: Option 'D'

Answer: Option 'D' 
7p3 = 7 × 6 × 5 = 210