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- Question
- If n+2C 8 : n- 2P 4 = 57 : 16 then the value of n is?
Options- A. 20
- B. 19
- C. 18
- D. 17
- Correct Answer
- 19
Explanationn+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) - 1. 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
- 2. 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
- 3. 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
- 4. 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 Discuss
- 5. 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
- 6. Find the value of 5 P 2.
Options- A. 15
- B. 18
- C. 20
- D. 122 Discuss
- 7. If 50c r = 50c r + 2 find r.
Options- A. 24
- B. 23
- C. 22
- D. 21 Discuss
- 8. If nP 3 = 9240, then find the value of n.
Options- A. 20
- B. 21
- C. 22
- D. 23 Discuss
- 9. In how many different ways, can the letters of the word 'INHALE' be arranged?
Options- A. 720
- B. 360
- C. 120
- D. 650 Discuss
- 10. In how many ways, the letters of the word 'ARMOUR' can be arranged?
Options- A. 720
- B. 300
- C. 640
- D. 350 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 28
Explanation:
Required no. of hand shakes = {8 x (8 - 1)}/2 = 28
Correct Answer: 2300
Explanation:
Required number of ways = 25C3
= (25 x 24 x 23) / (1 x 2 x 3) = 2300
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: 5005
Explanation:
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
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: 20
Explanation:
5 P2 = 5! / (5 - 2)! = 5 x 4 = 20
Correct Answer: 24
Explanation:
By formula, ncx = ncy
? x = y or x + y = n
Now, 50cr = 50cr + 2
? r + r + 2 = 50 or r = r + 2
? 2r = 48 [? r = r + 2 is not possible]
? r = 24
Correct Answer: 22
Explanation:
nP3 = 9240 ? n! / (n-3)! = 9240
? n(n - 1)(n - 2) = 9240
? n(n - 1)(n - 2) = 22 x 21 x 20
? n = 22
Correct Answer: 720
Explanation:
The word 'INHALE' has 6 distinct letters.
? Number of arrangements = n ! = 6 !
= 6 x 5 x 4 x 3 x 2 x 1
= 720
Correct Answer:
Explanation:
Number of arrangements n ! /( p ! q ! r ! )
Total letters = 6, but R has come twice.
So, required number of arrangements
= 6 ! / 2 ! = (6 x 5 x 4 x 3 x 2 !) / 2 ! = 360
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