# 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
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
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
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