A five letter word is to be formed such that the letters appearing in the odd numbered positions are

Question

A five letter word is to be formed such that the letters appearing in the odd numbered positions are taken from the letters which appear without repetition in the word ″MATHEMATICS″. Further the letters appearing in the even numbered positions are taken from the letters which appear with repetition in the same word ″MATHEMATICS″. The number of ways in which the five letter word can be formed is:

Accepted Answer

There are 2M, 2T, 2A and 1 H, E, I, C, S
First find the number of ways if odd’s no. position place be filled is ⁵p₃ = 60
Now Case I If even place words is same i.e no. of ways = 3
Case II If even place words is different i.e no. of ways = ³c₂ × 2! = 6
Hence total no. of arragment is
60 × (3 + 6) = 540

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