RRB NTPC - Permutations Combinations

1.

If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE. 

   A.) 142
   B.) 141
   C.) 114
   D.) None of these

Answer: Option 'C'

Answer: Option 'C' 
Total no'of arrangements 5P5  = 5! = 120 
no'of arrangements start with AE = 1 × 6 = 6 
no'of arrangements which do not start with AE = 120 - 6 = 114.

2.

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

3.

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.

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.

Find 4C2?

   A.) 5
   B.) 6
   C.) 8
   D.) 9

Answer: Option 'B'

4C2
= 4!/(4-2)!2!
= 4!/(2! × 2!)
= (4 × 3)/2 = 6.

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