Question

Q-How many different 5-card hands can be dealt from a standard 52-card deck?

Q How many different passwords of length 8 can be made if there must be one upper-caseletter, one lower-case letter, and 6 digits?2.

Answer 1

Q-How many different 5-card hands can be dealt from a standard 52-card deck?

The cards to be picked without replacement from the deck of 52

Hence, we will pick 5 cards out of 52 using combination

Number of different card hand = 52C5

Number of different card hand = 52! / (5!* 47! )

Number of different card hand = 311875200 / 5*4*3*2*1

Number of different card hand = 2598960

Q How many different passwords of length 8 can be made if there must be one upper-case letter, one lower-case letter, and 6 digits?

Number of upper-case letter = 26

Number of lower-case letter = 26

Number of digits = 10

The combinations can be formed just by multiplying

Number of combination = Number of upper-case letter*Number of lower-case letter*Number of digits

Number of combination = 26*26*10

Number of combination = 6760