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- Question
- How many groups of 6 persons can be formed from 8 men and 7 women?
Options- A. 5000
- B. 5005
- C. 5050
- D. None of these
- Correct Answer
- 5005
ExplanationTotal 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. If 56P r + 6 : 54P r + 3 = 30800 : 1 then the value of r is?
Options- A. 40
- B. 41
- C. 42
- D. None of these Discuss
- 2. If three marbles are picked at random, what is the probability that at least one is blue?
Options- A. 7/12
- B. 37/44
- C. 5/12
- D. 7/44 Discuss
- 3. If a 4- digit number is formed at random using the digit 1, 3, 5, 7 and 9 without repetition, then the probability that it is divisible by 5, is
Options- A. 4/5
- B. 3/5
- C. 1/5
- D. 2/3 Discuss
- 4. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was four is
Options- A. 2/5
- B. 1/5
- C. 1/6
- D. None of these Discuss
- 5. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target atleast three times, is
Options- A. 291/364
- B. 371/464
- C. 471/502
- D. 459/512 Discuss
- 6. There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket?
Options- A. 125
- B. 140
- C. 110
- D. 120 Discuss
- 7. There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed.?
Options- A. 2200
- B. 2300
- C. 2400
- D. 3200 Discuss
- 8. 8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes?
Options- A. 16
- B. 36
- C. 56
- D. 28 Discuss
- 9. If n+2C 8 : n- 2P 4 = 57 : 16 then the value of n is?
Options- A. 20
- B. 19
- C. 18
- D. 17 Discuss
- 10. Find the value of 5 P 2.
Options- A. 15
- B. 18
- C. 20
- D. 122 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 41
Explanation:
? 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
Correct Answer: 37/44
Explanation:
Total number of possible outcomes
= 12C3 = 220
Number of events which do not contain blue marbles (3 marbles out of 7 marbles) = 7C3 = 35
? Required probability = 1 - 35/220 = 37/44
Correct Answer: 1/5
Explanation:
Number of 4- digit numbers which are formed with 1, 3, 5, 7, 9 = 5P4
= 5 x 4 x 3 x 2 = 120 = n (s)
Number of 4 digit number which are formed with 1, 3, 5, 7, 9 and are divisible by 5 = 4P3
= 4 x 3 x 2 = 24 = n (E)
? p(E) = n(E)/n( s) = 24/120
= 1/5
Correct Answer: None of these
Explanation:
Total number of favourable outcomes n(S) = 63 = 216
Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6), (5, 4, 6), ( 6, 5, 4), (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5),(6, 6, 3), (6, 3, 6), (3, 6, 6)
Now, outcomes on which first roll was a four, n(E) = (4, 5, 6),(4, 6, 5)
? P(E) = n(E)/n(S) = 2/216 =1/108
Correct Answer: 459/512
Explanation:
Required Probability
Given, n = 5 and r = 3
Then, Success P = 3/4
Failure, q = 1 - 3/4 = 1/4
Man hit the target thrice
= 5c3 (3/4)3 (1/4)2 + 5c4 (3/4)3 (1/4) + 5c3(3/4)5
= (270/1024) + (405/1024) + (243/1024)
= 918/1024
= 459/512
Correct Answer: 120
Explanation:
Required number of ways = 10C3
= 10!/ {3! (10 - 3)!} = 10! / (3! 7!) = (10 x 9 x 8) / (3 x 2) = 120
Correct Answer: 2300
Explanation:
Required number of ways = 25C3
= (25 x 24 x 23) / (1 x 2 x 3) = 2300
Correct Answer: 28
Explanation:
Required no. of hand shakes = {8 x (8 - 1)}/2 = 28
Correct Answer: 19
Explanation:
n+2C8 : n-2P4 = 57 : 16
? {(n + 2 )! (n - 6)!} / {(n - 6)! (n - 2)! 8!} = 57/16
? (n + 2) (n + 1) n(n - 1) = 143640
? (n2 + n - 2) (n2 + n ) = 143640
? (n2 + n )2 - 2(n2 + n) + 1 = 143641
? (n2 + n - 1)2 = (379)2
[? n2 + n - 1 > 0]
? n2 + n - 1 = 379
? n2 + n - 380 = 0
? (n + 20) (n - 19) = 0
?n = 19 ( Since n is not negative)
Correct Answer: 20
Explanation:
5 P2 = 5! / (5 - 2)! = 5 x 4 = 20
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