1.From a group containing 4 men, 6 women, and 5 children, in how many different ways can you choose 3 men, 2 women, and 3 children?
2.From a group containing 4 men, 6 women, and 5 children, in how many different ways can you choose 2 men, 3 women, and 1 child?
3.How many different ways can the letters of the word "MATERIAL" be arranged so that all the vowels appear together?
4.How many distinct new arrangements can be created by rearranging the letters in the word 'ALIVE'?
5.From a group consisting of 3 women and 5 men, how many different 5-member teams can be created if two specific women must always be part of the team?
6.In how many different orders can 7 players throw a ball such that the youngest player does not throw it last?
7.How many different ways can five boys and three girls be seated in a row if all the boys must sit together?