Answer
4. n = 30, r = 8
(■(A@B)) = (A choose B)
a. (■(30+8-1@30))
= (■(37@30))=37!/(30!*7!)
= (31*32*33*34*35*36*37)/(2*3*4*5*6*7)
= 10295472
b. (■(26+8-1@26))
= (■(33@26))
= 33!/(26!*7!)
= (27*28*29*30*31*32*33)/(2*3*4*5*6*7)
= 4272048
c. [ways with inventory of 30 batteries and at most 3 A7b batteries]
= [ways with inventory of 30 batteries] – [ways with inventory of 30 batteries and at least 4 A7b batteries]
= (■(37@30))- (■(33@26))
= 10295472- 4272048
= 6023424
Work Step by Step
4. n = 30, r = 8
(■(A@B)) = (A choose B)
a. (■(30+8-1@30))
= (■(37@30))=37!/(30!*7!)
= (31*32*33*34*35*36*37)/(2*3*4*5*6*7)
= 10295472
b. (■(26+8-1@26))
= (■(33@26))
= 33!/(26!*7!)
= (27*28*29*30*31*32*33)/(2*3*4*5*6*7)
= 4272048
c. [ways with inventory of 30 batteries and at most 3 A7b batteries]
= [ways with inventory of 30 batteries] – [ways with inventory of 30 batteries and at least 4 A7b batteries]
= (■(37@30))- (■(33@26))
= 10295472- 4272048
= 6023424