Permutations Combinations

  • 1. 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

  • 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. 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'

  • 4. In how many different ways can the letters of the word "CLAIM" be rearrangement? 
A.) 120
B.) 125
C.) 130
D.) None of these

Answer: Option 'A'

Answer: Option 'A' 
The total number of arrangements is 
5P5  = 5! = 120

  • 5. 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.