First slide

Permutations

Question

Suppose that six students, including Madhu and Puja, are having six beds arranged in a row. Further, suppose that Madhu does not want a bed adjacent to Puja. Then the number of ways, the beds can be allotted to students is

Moderate

A

264
B

480
C

600
D

384

Solution

Number of ways of arranging beds $=^{6} P_{6} = 6! = 720$
Number of ways in which Madhu and Puja have theire beds together is $(2) (^{5} P_{5}) = 2 (5!) = 240$
Thus, required number of ways $= 720 - 240 = 480$

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