a2zinterviews

16.	How many arrangements can be mado out of the letters of the word 'ENGINEERING' ?
	A.  277200
	B.  92400
	C.  69300
	D.  23100

Solution

The word 'ENGINEERING' contains 11 letters, namely 3E, 3N, 2G, 2I and 1R. Required number of arrangements = 11 ! / (3!)(3!)(2!)(2!)(1!) ‹=› 277200.

17.	Evaluate : 30! / 28!
	A.  550
	B.  610
	C.  870
	D.  920

Solution

We have 30! / 28! = 30 x 29 x (28!) / 28! = (30 x 29) = 870.

18.	In how many different ways can the letters of the word ‘Banking’ be arranged so that the vowels always come together?
	A.  240
	B.  360
	C.  480
	D.  720

Solution

In the word ‘Banking’, we treat the two vowels AI as one letter. Thus, we have BNKNG (AI). This has 6 letters of which N occurs 2 times and the rest are different. Number of ways of arranging these letters = 6! / (2!)(1!)(1!)(1!)(1!) ‹=›360. Now, 2 vowels AI can be arranged in 2! = 2 ways. Required number of ways = (360 x 2) ‹=› 720.

19.	Find the value of 4P4
	A.  12
	B.  14
	C.  16
	D.  24

Solution

4P4 = 4! = (4 x 3 x 2 x 1) = 24.

20.	Find the value of 50C50
	A.  0
	B.  1
	C.  2
	D.  3

Solution

50C50 = 1. Therefore nCn = 1.