SELF DOUBT

Question

If the number of ways of selecting K coupons out of an unlimited number of coupons bearing the letters A , T , M so that they cannot be used to spell the word MAT is 93 , the K equals to _______________.

a) 3      b) 5          c)   7      d) None

Comments

I am getting k as 31. What is the answer?

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answer given as 5

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I am also getting 31..

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@minipanda i m getting 5

Here , A , T , M bears unlimited no of coupons .

Thus selecting K in which word MAT is not spelled

if atleast one letter is not selected i.e 3C1

From the remaining two we have to select K i.e for each selection of K coupons we have 2 ways

for K coupons we have 2^k ways but to select atleast one 2^k-1

Words cannot be used to spell mat = 3(2^k-1)

And by condition

3(2^k-1) = 93.................    solving this k = 5

Correct if wrong