Permutation and Combination problems
- 1. Find the value of 5 P 2.
Options- A. 15
- B. 18
- C. 20
- D. 122 Discuss
Correct Answer: 20
Explanation:
5 P2 = 5! / (5 - 2)! = 5 x 4 = 20
- 2. If 50c r = 50c r + 2 find r.
Options- A. 24
- B. 23
- C. 22
- D. 21 Discuss
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
- 3. If nP 3 = 9240, then find the value of n.
Options- A. 20
- B. 21
- C. 22
- D. 23 Also asked in: Bank Exams, Bank PO
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
- 4. In how many different ways, can the letters of the word 'INHALE' be arranged?
Options- A. 720
- B. 360
- C. 120
- D. 650 Discuss
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
- 5. In how many ways, the letters of the word 'ARMOUR' can be arranged?
Options- A. 720
- B. 300
- C. 640
- D. 350 Discuss
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
- 6. In how many ways, the letters of the word 'STRESS' can be arranged?
Options- A. 360
- B. 240
- C. 720
- D. 120 Discuss
Correct Answer: 120
Explanation:
Required number of arrangements = 6 ! / 3 ! [? S has come thrice ]
= [ 6 x 5 x 4 x 3! ] /3 !
= 120
- 7. In how many ways, the letters of the word 'BANKING' can be arranged?
Options- A. 5040
- B. 2540
- C. 5080
- D. 2520 Discuss
Correct Answer: 2520
Explanation:
Total letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !
= [7 x 6 x 5 x 4 x 3 x 2 ! ] / 2 ! = 2520
- 8. In how many different ways, the letters of word 'FINANCE' can be arranged?
Options- A. 5040
- B. 2040
- C. 2510
- D. 4080 Discuss
Correct Answer:
Explanation:
Total number of letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !
= [7 x 6 x 5 x 4 x 3 x 2! ] / 2!
= 2520
- 9. In how many different ways, can the letters of the word 'VENTURE' be arranged?
Options- A. 840
- B. 5040
- C. 1260
- D. 2520 Discuss
Correct Answer: 2520
Explanation:
The required different ways = 7 ! / 2 !
= 7 x 6 x 5 x 4 x 3 x 2!/2!
= 2520
- 10. In a meeting between two countries, each country has 12 delegates. All the delegates of one country shake hands with all delegates of the other country. Find the number of handshakes possible?
Options- A. 72
- B. 144
- C. 288
- D. 234 Discuss
Correct Answer: 144
Explanation:
Total number of handshakes = 12 x 12 = 144
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