Permutation and Combination Questions Answers

Permutation and Combination Questions Answers (MCQ) listings with explanations includes questions on calculating combinations, permutations by different tricks which are important for many competitive exams.

11) In how many way the letter of the word 'RUMOUR' can be arran

  • 1) 2520
  • 2) 480
  • 3) 360
  • 4) 180
View Answer View Explanation
Ans.   D
Explanation :
In above word, there are 2 'R' and 2 'U' So Required number will be \begin{aligned} = \frac{6!}{2!*2!} \\ = \frac{6*5*4*3*2*1}{4} \\ = 180 \end{aligned}

12) How many words can be formed from the letters of the word 'SIGNATURE' so that vowels always come togeth

  • 1) 17280
  • 2) 4320
  • 3) 720
  • 4) 80
View Answer View Explanation
Ans.   A
Explanation :
word SIGNATURE contains total 9 letters. There are four vowels in this word, I, A, U and E Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now So total letter are 6. 6 letters can be arranged in 6! ways = 720 ways Vowels can be arranged in themselves in 4! ways = 24 ways Required number of ways = 720*24 = 17280

13) In how many ways can the letters of the word 'CORPORATION' be arranged so that vowels always come togeth

  • 1) 5760
  • 2) 50400
  • 3) 2880
  • 4) None of above
View Answer View Explanation
Ans.   B
Explanation :
Vowels in the word 'CORPORATION' are O,O,A,I,O Lets make it as CRPRTN(OOAIO) This has 7 lettes, where R is twice so value = 7!/2! = 2520 Vowel O is 3 times, so vowels can be arranged = 5!/3! = 20 Total number of words = 2520 * 20 = 50400

14) In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be th

  • 1) 109
  • 2) 128
  • 3) 138
  • 4) 209
View Answer View Explanation
Ans.   D
Explanation :
In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there. So we can have (four boys) or (three boys and one girl) or (two boys and two girls) or (one boy and three gils) This combination question can be solved as \begin{aligned} (^{6}{C}_{4}) + (^{6}{C}_{3} * ^{4}{C}_{1}) + \\ + (^{6}{C}_{2} * ^{4}{C}_{2}) + (^{6}{C}_{1} * ^{4}{C}_{3}) \ = \left[\dfrac{6 \times 5 }{2 \times 1}\right] + \left[\left(\dfrac{6 \times 5 \times 4 }{3 \times 2 \times 1}\right) \times 4\right] + \\\left[\left(\dfrac{6 \times 5 }{2 \times 1}\right)\left(\dfrac{4 \times 3 }{2 \times 1}\right)\right] + \left[6 \times 4 \right] \= 15 + 80 + 90 + 24\= 209 \end{aligned}
<< Previous Page Next Page >>

Get Free Current Affairs and Govt Jobs Alerts in your mailbox

Current Affairs
Govt Jobs

Visit Our Blog