MATH SOLVE

2 months ago

Q:
# From a shipment of 65 transistors, 6 of which are defective, a sample of 5 transistors is selected at random.(a) In how many different ways can the sample be selected?________ways(b) How many samples contain exactly 3 defective transistors?________samples(c) How many samples do not contain any defective transistors?________ samples

Accepted Solution

A:

Answer:a) 8259888b) 34220c) 45057474Step-by-step explanation:Given,The total number of transistor = 65,In which, the defective transistor = 6,So, the number of non defective transistor = 65 - 6 = 59,Since, out of these transistor 5 are selected,a) Thus, the number of ways = the total possible combination of 5 transistors = [tex]{65}C_ 5[/tex][tex]=\frac{65!}{(65-5)!5!}[/tex][tex]=8259888[/tex]b) The number of samples that contains exactly 3 defective transistors = the possible combination of exactly 3 defective transistors = [tex]{6}C_3\times {59}C_2[/tex][tex]=\frac{6!}{(6-3)!3!}\times \frac{59!}{(59-2)!\times 2!}[/tex][tex]=20\times 1711[/tex][tex]=34220[/tex]c) The number of sample without any defective transistor = The possible combination of 0 defective transistor = [tex]^6C_0\times ^{59}C_5[/tex][tex]=1\times 45057474[/tex][tex]=45057474[/tex]