00:01
In this problem we are provided with a standard deck of 52 cards and we are asked to draw an 8 card hand.
00:14
In subpart a, we have to find out the probability p such that all the 8 cards are black cards only.
00:31
Let us denote this event by a.
00:36
So therefore we need to calculate p of a which equals to.
00:40
To n of a over n of s.
00:45
So, n of a is the total number of favorable outcomes and n of s is the total number of possible outcomes.
00:58
So the total number of favorable outcomes is 26 c8 since there are 26 black cards and we need to pick out eight cards from them.
01:11
And n of s is the total number of possible outcomes.
01:16
So in this case it is 52c8 since we have 52 cards and we need to pick out an 8 card hand.
01:25
We know that ncr equals to n factorial over r factorial times n minus r factorial.
01:35
So substituting in the formula we have 26c8 to be 26 factorial divided by 8 factorial times 26 minus 8 which is 18.
01:49
So we have 18 factorial.
01:51
The whole divided by 52c8 which would be 52 factorial over 8 factorial times 44 factorial.
02:02
So simplifying this and evaluating it we get 156 double 275 for 26c8 and for 52 .8 and for 52 we have 752538 150.
02:24
Simplifying it further, we obtained 209 divided by 100674...