a2zinterviews

11.	In how many ways can the letters of the word 'APPLE' be arranged?
	A.  720
	B.  120
	C.  60
	D.  180

Solution

The word 'APPLE' contains 5 letters, 1A, 2P, 1L and 1E. Required number of ways = 5! / (1!) (2!) (1!) (1!) ‹=› 60.

12.	How many word can be formed by using all the letters of the word, 'ALLAHABAD'?
	A.  3780
	B.  1890
	C.  7560
	D.  2520

Solution

The word 'ALLAHABAD' contains 9 letters, namely 4A, 2L, 1H, 1B, and 1D. Required number = 9! / (4!) (2!) (1!) (1!) (1!) = 7560.

13.	A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
	A.  48
	B.  64
	C.  69
	D.  71

Solution

we may have(1 black and 2 non-black) or ( 2 black and 1 non black) or ( 3 black). Required number of ways ‹=›(3C1 × 6C2) + (3C2 ˜6C1) + (3C3) ‹=›(3 x 6 x 5 / 2 x 1) + (3 x 2 / 2 x 1 x 6) + 1 ‹=› (45 + 18 + 1) = 64.

14.	In how many different ways can the letters of the word 'AUCTION' be arranged in such a way that the vowels always come together?
	A.  30
	B.  48
	C.  144
	D.  576

Solution

The word Auction has 7 different letters. When, the vowels AUIO are always together, they can be supposed to form one letter. Then, we have to arrange the letters CTN (AUIO). Now, 4 letters can be arranged in 4! = 24 ways. The vowels (AUIO) can be arranged in 4!= 24 ways. Required number of ways = (24 x 24) = 576.

15.	How many words can be formed from the letters of the word 'SIGNATURE' so that the vowels always come together?
	A.  720
	B.  1440
	C.  2880
	D.  17280

Solution

The word SIGNATURE has 9 different letters. When, the vowels IAUE are always together, they can be supposed to form one letter. Then, we have to arrange the letters SGNTR (IAUE). These 6 letters can be arranged in 6P6= 6 ! = 720 ways. The vowels (IAUE) can be arranged in 4P4 = 4! = 24 ways. Required number of ways = (720 x 24) = 17280..