Answer :
Answer:
Total number of ways a hotel can purchase 5 of 12 sets and receive at least 2 defective sets = 288
Step-by-step explanation:
P.S - The exact question is -
Given - A shipment of 12 television sets contains 3 defective sets.
To find - In how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?
Proof -
We know that The combination of n distinct objects taken k at a time is
[tex]^{n} C_{k} = \frac{n!}{k! (n-k)!}[/tex]
Now,
The number of ways hotel can receive 2 defective sets among 5 that can be purchased is
[tex]^{9} C_{3} * ^{3}C_{2} = \frac{9!}{3! (9-3)!} \frac{3!}{2! (3-2)!}[/tex]
⇒[tex]^{9} C_{3} * ^{3}C_{2}[/tex] = 84(3) = 252
Now,
The number of ways that hotel receives 3 defective sets among 5 that are purchased is
[tex]^{9} C_{2} * ^{3}C_{3} = \frac{9!}{2! (9-2)!} \frac{3!}{3! (3-3)!}[/tex]
⇒[tex]^{9} C_{2} * ^{3}C_{3}[/tex] = 36(1) = 36
Now,
Total number of ways a hotel can purchase 5 of 12 sets and receive at least 2 defective sets = 252 + 36 = 288
⇒Total number of ways a hotel can purchase 5 of 12 sets and receive at least 2 defective sets = 288
