Permutations Combinations

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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

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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

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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'

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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

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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.

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6.

How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word? 

   A.) 7 ways
   B.) 6 ways
   C.) 5 ways
   D.) 2 ways

Answer: Option ''

Answer: Option 'B' 
E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways

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7.

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.

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8.

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.

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9.

Find 9P3

   A.) 414
   B.) 514
   C.) 504
   D.) None of these

Answer: Option 'B'

9P3 = 9!/6! = 9 × 8 × 7
= 504.

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10.

Find 7P7

   A.) 4440
   B.) 5040
   C.) 5045
   D.) None of these

Answer: Option 'B'

7P7 = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

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