Question

A man just bought 4 suits, 8 shifts, and 12 ties.

A) If he selects one suit, one shirt, and one tie at random the next day, how many outfit options does he have?
B) He needs three different shirts for his upcoming business trip. In how many ways can he pick the shirts?
C) If he also needs three ties, in how many ways can he pick three shirts AND three ties? Assume each tic can go with every shirt.

Answer 1

A). Number of ways he can select one suit, one shirt and one tie = 384

B). Number of ways he can pick 3 shirts = 56

c). Number of ways he can select 3 shirts and 3 ties = 12320

Explanation:

A man just bought 4 suits, 8 shirts and 12 ties.

A). Number of ways, he can select one suit = 4

Number of ways, he can select one shirt = 8

And number of ways, he can select one tie = 12

Total number of ways he can select one suit, one shirt and one tie

= 4×8×12

= 384 ways

B). To select three different shirts out of 8 shirts, number of combinations will be =
`^(8)C_(3)`

=
`(8!)/(3!(8-3)!)`

=
`(8* 7* 6)/(3* 2)`

= 56 ways

C). If he needs to pick three shirts AND three ties,

Number of ways he picks 3 shirts =
`^(8)C_(3)`

= 56 ways [Already seen in part B]

Number of ways he can select 3 ties =
`^(12)C_(3)`

=
`(12!)/(3!(12-3)!)`

=
`(12!)/(9!* 3!)`

=
`(12* 11* 10)/(3* 2)`

= 220

Therefore, number of ways he can select 3 shirts and 3 ties = 56×220

= 12320 ways