- #1
Addez123
- 199
- 21
- TL;DR Summary
- What are the odds of getting 5 spades, 3 hearts, 3 diamonds, 2 clubs when drawing cards at random (Without putting them back).
The odds are $$\frac {13C5 \times 2 \times 13C3 \times 13C2} {52C13}$$
This is correct according to my book. The follow up question then becomes, what if you can pick 5 of any suit, 3 of any other suit, another 3 from the remaining 2 suits and 2 from the last untouched suit?
The solution would be to calculate
4C1 * 13C5 for the first suit, then 3C1 *13C3 for second suit etc..
Basically same answer as first question except times: 4C1 * 3C1 * 2C1 * 1C1 = 24
Textbook says the correct aswer is same answer as first question * 12, not 24.
That is what I need help with, why 12?
This is correct according to my book. The follow up question then becomes, what if you can pick 5 of any suit, 3 of any other suit, another 3 from the remaining 2 suits and 2 from the last untouched suit?
The solution would be to calculate
4C1 * 13C5 for the first suit, then 3C1 *13C3 for second suit etc..
Basically same answer as first question except times: 4C1 * 3C1 * 2C1 * 1C1 = 24
Textbook says the correct aswer is same answer as first question * 12, not 24.
That is what I need help with, why 12?