Answer:
a) there are 7,854,000 number of ways the random selections can be arranged
b) the required probability is 0.0445
Step-by-step explanation:
Given that;
you have 12 pair of long pants, 6 pair of short pant and 17 t-shirt which in total;
Total = 12 + 6 + 17 = 35
a) number of ways a random selection of 9 pair of long pants, 4 pair of short pants and 13 t-shirts can be arranged;
⇒ [ 12 × [ 6 × [ 17
9 ] 4 ] 13 ]
= (12! / (9! 3!)) (6! / (4! 2!)) (17! / (13! 4!))
= (220) (15) (2380)
= 7,854,000
Therefore there are 7,854,000 number of ways the random selections can be arranged
b)
Number of ways of selecting 25 item from 35 items;
⇒ [ 35
25 ]
=
(35! / (25! 10!) = 183.579,396
now number of ways to select 10 pair of long pants, 3 pairs of short pantts and 12 t-shirt;
⇒ [ 12 × [ 6 × [ 17
10 ] 3 ] 12 ]
= (12! / (10! 2!)) (6! / (3! 3!)) (17! / (12! 5!))
= (66) (20) (6188)
= 8,168,160
So, Required probability = 8,168,160 / 183,579,396
= 0.0445
So the required probability is 0.0445
