5 boys and 6 girls attend a birthday party and play pin the tail on the donkey. If a girl wins first and second place and a boy wins third place, How many different arrangements of first, second, and third are there? =

75 Arrangements

Step-by-step explanation:

Girl can secure 1st & 3rd, boy can secure 2nd position in : 6 x 5 x 5 = 150 ways; As:

1st position holder can be chosen in 6 ways (among 6 girls) 2nd position holder can be chosen in 5 ways (among 5 boys) 3rd position holder can be chosen in (among 5 remaining girls)

The arrangement of first, second & third:

It is same : If Girl G1 gets first rank & Girl G2 gets third rank, is same as; Girl G1 gets third rank & Girl G2 gets first rank. So, two are considered the same group. Hence, number of arrangements are 150 / 2 = 75 arrangements.