Bunuel wrote:
In how many ways 8 different tickets can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
A. From 2 to 6 inclusive.
B. From 98 to 102 inclusive.
C. From 122 to 126 inclusive.
D. From 128 to 132 inclusive.
E. From 196 to 200 inclusive.
hi
I have seen a solution to a problem similar to this one elsewhere on the forum
let me explain it to you
since a total of 8 tickets is to be distributed to either Jane or Bill, 7 tickets can be distributed either to Jane or to Bill in
(1 + 1)*(1 + 1)*(1 + 1)*(1 + 1)*(1 + 1)*(1 + 1)*(1 + 1)
= 2*2*2*2*2*2*2 = 2^7 ways, and the arrangements will look like as under
0, 7
1, 6
2, 5
3, 4
4, 3
5, 2
6, 1
7, 0
here, as can be seen, in 2^7 ways, one person is getting even number of tickets and the other is receiving odd number of tickets, so
the remaining 1 ticket can be given to the one receiving odd number of tickets in only 1 way to entail the optimum arrangement where each buddy gets even number of tickets
so the answer is (2^7) * 1 = 128
hope this helps and is clear!
thanks
cheers, and do consider some kudos, guys