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show that the number of ways one can choose a set of distinct positive integers, each smaller than or equal to 50 ,such that their sum is odd,is 2^49
Dear pritam
we have 25 even number and 25 odd number
for sum to be odd ,we must select odd number of odd number .
so numere of ways =
25C0(25C1 +25C3+25C5+25C7 .........................+25C25)
+ 25C1(25C1 +25C3+25C5+25C7 .........................+25C25)
+ 25C2(25C1 +25C3+25C5+25C7 .........................+25C25)
.
+ 25C25(25C1 +25C3+25C5+25C7 .........................+25C25)
= (25C0 + 25C1 +25C2+25C3+25C4 .........................+25C25)(25C1 +25C3+25C5+25C7 ........................+25C25)
=225 .225-1
=249
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