Josephine develops her own rules for playing the game of poker. One of her rules is that you can have a hand called a “jojo” where all 5 cards are the same color. The probability you are dealt a “jojo” from a standard 52 card playing deck can be written in the form $$\frac{j \times _{26}C_{l}}{_{52}C_{n}}$$
What is the value of j + l + n ?

Question

Josephine develops her own rules for playing the game of poker. One of her rules is that you can have a hand called a “jojo” where all 5 cards are the same color. The probability you are dealt a “jojo” from a standard 52 card playing deck can be written in the form $$\frac{j \times _{26}C_{l}}{_{52}C_{n}}$$
What is the value of	j + l + n ?

anonymous · Answer

$$\frac{j \times _{26}C_{l}}{_{52}C_{n}} = \frac{j \times \frac{26!}{(26 - l)!l!}}{\frac{52!}{(52 - n)!n!}} = j \times \frac{26!}{(26 - l)!l!} \times \frac{(52 - n)!n!}{52!}$$
I got this far. What should I do now? @Wired

phi · Answer

I would not expand it.  I would try to figure out the probability of getting 5 cards of the same color from a standard deck

the denominator should be the number of hands with 5 cards.
the top is the number of hands with 5 cards of the same color.

phi · Answer

order does not matter for a "jojo"  so I would say 52C5 are the number of hands
so you know n=5
the number of red hands would be 26C5
same for black hands
so l=5
j=2
sum= 12

anonymous · Answer

$$_{52}C_{5}$$ = (52*51*50*49*48)/5! = 10*2*49*51*52
Is that for the denominator?

phi · Answer

yes, but the actual value is not important here.

phi · Answer

unless you are learning what M CHOOSE N means

phi · Answer

see my post up above

anonymous · Answer

THanks! I didn't think of doing that :)