Question

i have a hand that consists of 7 cards drawn from a standard 52 card deck. whats the probablity of having a hand with entirely cards that are not face cards/ an ace, or a hand with all clubs

Answer 1

There are total of 12 face cards and 4 aces

Hence there are 36 cards that are ne it er face cards not ace.

There are 13 clubs in a deck.

Probability of having a hand with entirely cards that are not face cards /an ace or a hand with all clubs

={ (36/52)*(35/51)*(34/50)*(33/49)*(32/48)*(31/47)*(30/46)} + { (13/52)*(12/51)*(11/50)*(10/49)*(9/48)*(8/47)*(7/46) }

(the number of cards decreases one by one, as we will be drawing a card without replacement, that is after drawing a card we won't put it back in the deck. Number of cards thst are neither face /ace or are clubs are decreasing one by one, as we want each of them in the 7 card, hence to get selected, those cards will also decrease one by one after they get selected)

= 0.0624