Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards, it contains (i) all Kings (ii) 3 Kings (iii) atleast 3 Kings.

Explanation

(i) as we know that 4 kings are there in 52 cards

P(3 kings)`= 0`

(ii) P(3 kings)`= (.^4C_3.^48C_4)/(.^52C_7)`

`= (4*(48*47*46*45)/(4*3*2*1))/((52*51*50*49*48*47*46)/(7*6*5*4*3*2*1))`

(iii) P(`>= 3`kings)= P( 3 kings) + P(4kings)

`= (.^4C_3 .^48C_4 + .^4C_4.^48C_3)/(.^52C_7)`

answer