Permutations And Combinations - MCQ 3 - Banking Exams MCQ

C) 60
Explanation: 0 0 0
Let these 3 circles are 3 fingers For 1st finger we have 5 choices, for second finger we have 4 choices left of rings, for third finger we have 3 choices left.
So total 5*4*3 = 60 ways

B) 720
Explanation: AUTHOR contains 6 letters, so total 6! ways.

A) 420
Explanation: MINIMUM contains 7 letters, so total 7! ways. But it contains 2 I’s and 3 M’s so divide by 2! And 3!
So ways 7!/(2! * 3!) = 7*6*5*4*3*2*1 / 2*1*3*2*1 = 420

D) 57624
Explanation: LEADING is 7 letters.
We have 4 places where letters are to be placed.
For first letter there are 7 choices, since repetition is allowed, for second, third and fourth letter also we have 7 choices each, so total of 7*7*7*7 ways = 2401 ways.
Now for arrangement of these 4 words, we have 4! Ways.
So total of 2401 * 4! Ways.

B) 2880
Explanation: 

First make IIIE in a circle. So we have Now we have N, V, S, B, L and box, their arrangements can be done in 6!
Letters inside circle are also to be arranged, we have I, I, I, E so ways are 4!/3!
Total ways 6! * 4!/3!

A) 1440
Explanation: In POUNDING, there are 8 places 1 2 3 4 5 6 7 8
So for 3 places selection of vowels, we have 1, 3, 5, 7 number places ⁴C₃ ways Now for arranging these 3 vowels, ways are 3!
Remaining 5 are consonants (in which there are 2 N’s) for which 5!/2! so total ways = ⁴C₃ *3!*(5!/2!)

B) 210
Explanation: We have to select 2 men from 4 men, and 4 women from 7 women So total ways = ⁴C₂ * ⁷C₄

C) 1722
Explanation: Case 1: 3 men and 2 women ⁸C₃ * ⁷C₂ = 1176
Case 2: 4 men and 1 women ⁸C₄ * ⁷C₁ = 490
Case 3: all 5 men ⁸C₅ = 56
Add all the cases.

D) 220
Explanation: There are total 13 people, a particular woman is to be included, so now 12 people are left to chosen from and 3 members to be chosen. So ways are ¹²C₃ .

B) 20
Explanation: Total 8 people, 2 men are to excluded, so 6 men left to be chosen from and 3 members to be chosen. So ways are ⁶C₃ .

Answer – B. 5¹⁰ × 4⁵
Explanation :
10 questions with 5 choices = 5¹⁰ 
20 questions with 4 choices =  4⁵

Answer – C.256 Explanation : 4*4*4*4 = 256

Answer – A.280 Explanation : 9!/[3! ×(3!)³ ] = 362880/6*216 = 280

Answer – D.56 Explanation :  ^9-1C_4-1 =  ⁸C₃ = 8*7*6/3*2*1 = 56

Answer – A.1320 Explanation : 12*11*10 = 1320

Answer – D.9000 Explanation : 8 letters = 8!/ 2! 2! = 40320/4 = 10080 6 letters = 6!/2! = 360 Vowels = 3!/2! =  3 No of ways vowels together = 360*3 = 1080 No of ways vowels not together = 10080 – 1080 = 9000

Answer – C. 2419200 Explanation :  ⁵P₃ * ⁸P₃ *   ⁶P₃ = 60*336*120 = 2419200

Answer – B.720 Explanation : 5!*3! = 120*6 = 720

Answer – D.72 Explanation : 3!*3! + 3!*3! = 36+36 = 72

Answer – A.1024 Explanation : No of way =4⁵ = 1024