## Permutation and Combination

#### Permutation and Combination

1. If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is ?
1. 40
2. 41
3. 42
4. None of these

1. 56Pr + 6 : 54Pr + 3 = 30800 : 1
⇒ 56! / (50 - r)! = (30800 x 54!) / (51-r!)

##### Correct Option: B

56Pr + 6 : 54Pr + 3 = 30800 : 1
⇒ 56! / (50 - r)! = (30800 x 54!) / (51-r!)
⇒ 56 x 55 = 30800/(51 - r)
⇒ 51 - r = 10
∴ r = 41

1. How many groups of 6 persons can be formed from 8 men and 7 women ?
1. 5000
2. 5005
3. 5050
4. None of these

1. Total no . of person = 8 + 7 = 15
No. of groups = 15C6

##### Correct Option: B

Total no . of person = 8 + 7 = 15
No. of groups = 15C6 = 15! / {6! (15 - 6)!} = 15! / (6! 9!)
= (15 x 14 x 13 x 12 x 11 x 10) / (6 x 5 x 4 x 3 x 2 x 1)
= 5005

1. There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket ?
1. 125
2. 140
3. 110
4. 120

1. Required number of ways = 10C3

##### Correct Option: D

Required number of ways = 10C3
= 10!/ {3! (10 - 3)!} = 10! / (3! 7!) = (10 x 9 x 8) / (3 x 2) = 120

1. There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed. ?
1. 2200
2. 2300
3. 2400
4. 3200

1. Required number of ways = 25C3

##### Correct Option: B

Required number of ways = 25C3
= (25 x 24 x 23) / (1 x 2 x 3) = 2300

1. 8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes ?
1. 16
2. 36
3. 56
4. 28

1. Required no. of hand shakes = {8 x (8 - 1)}/2 = 28

##### Correct Option: D

Required no. of hand shakes = {8 x (8 - 1)}/2 = 28