a2zinterviews

21.	In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together?
	A.  720
	B.  360
	C.  1440
	D.  13440

Solution

The word 'SOFTWARE' contains 8 letters. When the vowels OAE are always together, they can be supported to form one letter. Thus, we have to arrange the letters SFTWR (OAE). Now, 5 letters can be arranged in 6! = 720 ways. The vowels (OAE) can be arranged among themselves in 3! = 6 ways. Therefore required number of ways = (720 x 6) = 4320.

22.	Find the value of 10C3
	A.  30
	B.  60
	C.  90
	D.  120

Solution

10C3 = 10 x 9 x 8 / 3! = 10 x 9 x 8 / 3 x 2 x 1 = 120.

23.	In how many different ways can the letters of the word ‘LEADING’ be arranged in such a way that the vowels always come together?
	A.  360
	B.  480
	C.  530
	D.  720

Solution

The word 'LEADING' contains 7 letters. When the vowels EAI are always together, they can be supported to form one letter. Then, we have to arrange the letters LDNG (EAI). Now, 5 letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Therefore required number of ways = (120 x 6) = 720.