Please help with all parts and show work Thanks Decks of Pin

Please help with all parts and show work. Thanks!

Decks of Pinochle cards have a total of 48 cards and consist of 8 cards each of nines, tens, jacks, queens, kings, and aces with there being two of each suit of each denomination (for example, there are 2 aces each of diamonds, clubs, hearts, and spades for the total of 8 aces). Suppose that you are dealt a 7-card hand from a deck of Pinochle cards. What is the probability that:

a) you are dealt at most 2 clubs?

b) you are dealt exactly 1 ten?

Solution

a) PROBABILITY THAT you are dealt at most 2 clubs...

Here ,7 cards are choosen from 48..so, n = 7..
let, x = no. of clubs in my hands...
so,atmost 2 clubs means x <=2...

total number of clubs in the deck of 48 cards = 12...
so, probability of picking a club = 12/ 48 = 1/4...
so, define success = picking a club..prob. of success = 1/4.......

prob[ at most 2 clubs ] = p[ exactly 2 clubs] + p [ exactly 1 club] + p [ no club]
=( 7 C 2) ( 1/4 ) ^ 2 * ( 3/4) ^ 5 + ( 7 C 1) ( 1/4)^1*( 3/4) ^6 + ( 7 C 0) (1 /4 ^ 0 8 ( 3/4)^7
= 0.311462402+0.311462402 + 0.13348388671875 = 0.756408691.....

B) Success = picking a ten..
prob. of success = total numbers of 10 / total no. of cards = 12 / 48 = 1/4...

prob. [ DEALT EXACTLY 1 TEN ] = ( 7 C 1) ( 1/4)^1 * ( 3/4)^6 = 0.31146240234375....