RRB NTPC - Permutations Combinations

1.

In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together. 

   A.) 720
   B.) 5040
   C.) 4320
   D.) None of these

Answer: Option 'A'

Answer: Option 'A'

2.

In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee. 

   A.) 10
   B.) 46
   C.) 56
   D.) None of these

Answer: Option 'B'

1W 2M      2W 1M           3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
Atleast one women = total - with out women
Atleast one women = 56 - 10 = 46

3.

In how many different number of ways the letters of the word 'ENGINEERING' can be arranged.

   A.) 27200
   B.) 27700
   C.) 277200
   D.) 27720

Answer: Option 'C'

11!/(3! × 3! × 2! × 2! × 1!)
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(3 × 2 × 3 × 2 × 2 × 2 × 1)
= 11 × 10 × 8 × 7 × 5 × 3
= 277200

4.

In how many different number of ways 4 boys and 2 girls can sit on a bench?

   A.) 620
   B.) 640
   C.) 720
   D.) None of these

Answer: Option ''

Answer: Option 'C'
npn = n! 
6p6
= 6 × 5 × 4 × 3 × 2 × 1 = 720

5.

Find 102C99?

   A.) 71700
   B.) 17100
   C.) 17170
   D.) 171700

Answer: Option 'B'

102C99
= 102!/(102-99)!99!
= 102!/(3! × 99!)
= (102 × 101 × 100)/(3 × 2)

34 × 101 × 50 = 171700.

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