Answer
a. (16 choose 7)
= 16!/7!(9!)
= 10*11*12*13*14*15*16/(2*3*4*5*6*7)
= 10*11*13*8
= 11440
b. (16 choose 13) + (16 choose 14) + (16 choose 15) + (16 choose 16)
= 16!/13!3! + 16!/14!2! + 16!/15! + 1
= 14*15*16/2*3 + 15*16/2 + 16 + 1
= 7*5*16 + 15*8 + 16 + 1
= 560 + 120 + 16 + 1
= 697
c. [total bit strings] – [total bit strings that don’t contain 1]
= 216 - (16 choose 0)
= 216 – 16!/0!(16!)
= 216 – 1
= 65535
d. (16 choose 1) + (16 choose 0)
= 16!/1!(15!) + 1
= 16 + 1
= 17
Work Step by Step
a. (16 choose 7)
= 16!/7!(9!)
= 10*11*12*13*14*15*16/(2*3*4*5*6*7)
= 10*11*13*8
= 11440
b. (16 choose 13) + (16 choose 14) + (16 choose 15) + (16 choose 16)
= 16!/13!3! + 16!/14!2! + 16!/15! + 1
= 14*15*16/2*3 + 15*16/2 + 16 + 1
= 7*5*16 + 15*8 + 16 + 1
= 560 + 120 + 16 + 1
= 697
c. [total bit strings] – [total bit strings that don’t contain 1]
= 216 - (16 choose 0)
= 216 – 16!/0!(16!)
= 216 – 1
= 65535
d. (16 choose 1) + (16 choose 0)
= 16!/1!(15!) + 1
= 16 + 1
= 17