Permutation and Combination
- If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is ?
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∵ 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
- How many groups of 6 persons can be formed from 8 men and 7 women ?
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Total no . of person = 8 + 7 = 15
No. of groups = 15C6Correct 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
- There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket ?
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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
- There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed. ?
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Required number of ways = 25C3
Correct Option: B
Required number of ways = 25C3
= (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 ?
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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