Complete question :
An electronics store receives a shipment of 35 graphing calculators, including 7 that are defective. 8 of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators?
Answer:
23535820 ways
3108105 ways
Explanation:
A.) How many selections can be made:
Number of ways of selecting 8 calculators from 35
35C8 :
Combination formula :
nCr = n! /(n-r)! r!
35C8 = 35! / (35-8)!8!
35C8 = 35! / 27! 8!
35C8 = (35*34*33*32*31*30*29*28) / (8*7*6*5*4*3*2*1)
35C8 = 948964262400 / 40320
= 23535820 ways
B.) number of non-defective calculators :
35 - 7 = 28
28C8 = n! /(n-r)! r!
28C8 = 28! / (28-8)!8!
28C8 = 28! / 20! 8!
28C8 = (28*27*26*25*24*23*22*21) / (8*7*6*5*4*3*2*1)
28C8 = 2506375872000 / 40320
= 3108105 ways