Question

Five cards are dealt from an ordinary deck of cards. Find the following. Assume ace is high. SHOW SET UP ONLY. DO NOT SOLVE.

How many hands are possible that contain only cards less than 8?

What is the probability of getting exactly 3 red cards, the jack of spades, and no other spades?

What is the probability of getting 2 of a kind and 2 of another kind?

Answer 1

1`) number of hands =n(selecting 5 cards from any of 4*7 =28 cards which are less then 8)=²⁸C₅

=28!/(5!*23!)=98280

2)

number of ways to get 3 red cards; jack of spades and 1 card from club =N(selecting 3 cards from 26 of red cards ; 1 card of jck of spades and 1 card from 13 cards of club)=²⁶C₃*1*¹³C₁ =2600*1*13=33800

hence probability= 33800/⁵²C₅ =33800/2598960

3)

( please revert for this part as card dealt are 5 and they have given description of only cards)