Permutation and Combination
 If ^{56}P_{r + 6} : ^{54}P_{r + 3} = 30800 : 1 then the value of r is ?

 40
 41
 42
 None of these

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∵ ^{56}P_{r + 6} : ^{54}P_{r + 3} = 30800 : 1
⇒ 56! / (50  r)! = (30800 x 54!) / (51r!)Correct Option: B
∵ ^{56}P_{r + 6} : ^{54}P_{r + 3} = 30800 : 1
⇒ 56! / (50  r)! = (30800 x 54!) / (51r!)
⇒ 56 x 55 = 30800/(51  r)
⇒ 51  r = 10
∴ r = 41
 How many groups of 6 persons can be formed from 8 men and 7 women ?

 5000
 5005
 5050
 None of these

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Total no . of person = 8 + 7 = 15
No. of groups = ^{15}C_{6}Correct Option: B
Total no . of person = 8 + 7 = 15
No. of groups = ^{15}C_{6} = 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
 There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket ?

 125
 140
 110
 120

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Required number of ways = ^{10}C_{3}
Correct Option: D
Required number of ways = ^{10}C_{3}
= 10!/ {3! (10  3)!} = 10! / (3! 7!) = (10 x 9 x 8) / (3 x 2) = 120
 There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed. ?

 2200
 2300
 2400
 3200

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Required number of ways = ^{25}C_{3}
Correct Option: B
Required number of ways = ^{25}C_{3}
= (25 x 24 x 23) / (1 x 2 x 3) = 2300
 8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes ?

 16
 36
 56
 28

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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