Question 13
Two children, Ann and Bob, play a game in which an ideal coin is tossed repeatedly. The chances to obtain heads or tails on each toss of this coin are equal. Ann throws the coin 3 times, while Bob throws the coin 5 times, independently of each other. Different orders of obtaining heads and tails are regarded as different results. Thus, there are $2\times2\times2=8$ different results for Ann and $2\times2\times2\times2\times2=32$ different results for Bob, so there are totally $8\times32=256$ different toss situations that both children obtain the number of heads. How many different situations are there so that both children obtain the same number of heads?