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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`
7 years ago

147 Points
```										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
Please  feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we  will get you  the answer and detailed  solution very  quickly.   We are all IITians and here to help you in your IIT JEE preparation.  All the best.   Regards, Askiitians Experts Badiuddin
```
7 years ago
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