Question

How many ways are there to form a committee of 50 members into 3 groups,where each group contain prime number of member??

Answer 1

50 is an even number. All prime numbers, greater than two, are odd numbers.

For three prime numbers to sum up to even number, one must be an even number and the other two must be odd numbers. Therefore, one group must consist of 2 memebers. That leaves us 48 members to divide into two groups, each one constisting of prime number of members.

I think the best way is to simply look at the list of the prime numbers up to the last one that is less than 48, which is 47, and check which two sums up to 48.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

And so,

43+5=48

41+7=48

37+11=48

31+17=48

29+19=48

Therefore, there are 5 ways.