Permutation and combination

If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, what is the minimum no. of mice’s required to find poisoned can?

a) 3 b) 2

c) 5 d) 1

ANS:

with 5 mice we can make 2^5 =32 possibilities ,In that first possibility no mice eat a can would be avoid other 31 combinations are used for test.

let A,B ,C,D and E be the mice,

0-indicate mice not eat that can

1-indicate mice eat that can

A B C D E

0 0 0 0 1 ---1st can

0 0 0 1 0----2nd can

0 0 1 0 0------3rd can

1 1 1 0 0......29th can

1 1 1 1 0......30th can

Above 30 combinatins are used for test poissined 'can' can which combination of mice is die.

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