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Maths-

General

Easy

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 repetitions in the same word MATHEMATICS. In how many different ways the five letter word can be formed -

390
600
540
450

The correct answer is: 540

In word MATHEMATICS
H, E, C, I and S – without repetition
M, A, T – occurs twice 5 letters can be placed on 3 places in ⁵P₃ ways.
Again even places 2^nd & 4^th position can be filled by the three letter M, A & T
Even places can be filled in two ways
³C₁ ways
³C₁ × 2! ways
Total ways ³C₁ + ³C₁ × 2! = 9 ways
Required number of ways = ⁵P₃ × 9 = 540 ways.

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