Respuesta :
Answer:
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
Step-by-step 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 = [tex]^{8}C_{3}[/tex]
= [tex]\frac{8!}{3!(8-3)!}[/tex]
= [tex]\frac{8\times 7\times 6}{3\times 2}[/tex]
= 56 ways
C). If he needs to pick three shirts AND three ties,
Number of ways he picks 3 shirts = [tex]^{8}C_{3}[/tex]
= 56 ways [Already seen in part B]
Number of ways he can select 3 ties = [tex]^{12}C_{3}[/tex]
= [tex]\frac{12!}{3!(12-3)!}[/tex]
= [tex]\frac{12!}{9!\times 3!}[/tex]
= [tex]\frac{12\times 11\times 10}{3\times 2}[/tex]
= 220
Therefore, number of ways he can select 3 shirts and 3 ties = 56×220
= 12320 ways
