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09 Dec 2015, 08:09
Kudos
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B
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Difficulty:
15%
(low)
Question Stats:
82% (01:23) correct
18%
(01:38)
wrong
based on 194
sessions
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In how many ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
A. 288
B. 144
C. 12
D. 48
E. 96
A. 288
B. 144
C. 12
D. 48
E. 96
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09 Dec 2015, 08:21
Kudos
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4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.
W_W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
W_W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
09 Dec 2015, 10:13
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Bunuel
Getting 144.
White piece will have to choose from only 4 places. It will have only 4 options to choose since the next piece to white must be black i.e they should be alternate.
WBWBWBW
So the first white piece can choose from 4 avai;labe options. second piece can choose from 3 available options ( after the first white pieces occupies its place) and so on....
Similarly, black pieces will have only 3 options to choose from. So the first piece can choose from 3 available positions, second will choose from 2 available positions....
so for white, the arrangement will be 4X3X2X1
for black , the arrangement will be 3X2X1
Combined, the arrangement will look like 4! X 3! which is equal to 144
