Answer:
The number of ways to select 5 diamonds and 3 clubs is 368,082.
Step-by-step explanation:
In a standard deck of 52 cards there are 4 suits each consisting of 13 cards.
Compute the probability of selecting 5 diamonds and 3 clubs as follows:
The number of ways of selecting 0 cards from 13 hearts is:
![{13\choose 0}=\frac{13!}{0!\times(13-0)!} =\frac{13!}{13!}=1](https://tex.z-dn.net/?f=%7B13%5Cchoose%200%7D%3D%5Cfrac%7B13%21%7D%7B0%21%5Ctimes%2813-0%29%21%7D%20%3D%5Cfrac%7B13%21%7D%7B13%21%7D%3D1)
The number of ways of selecting 3 cards from 13 clubs is:
![{13\choose 3}=\frac{13!}{3!\times(13-3)!} =\frac{13!}{13!\times10!}=286](https://tex.z-dn.net/?f=%7B13%5Cchoose%203%7D%3D%5Cfrac%7B13%21%7D%7B3%21%5Ctimes%2813-3%29%21%7D%20%3D%5Cfrac%7B13%21%7D%7B13%21%5Ctimes10%21%7D%3D286)
The number of ways of selecting 5 cards from 13 diamonds is:
![{13\choose 5}=\frac{13!}{5!\times(13-5)!} =\frac{13!}{13!\times8!}=1287](https://tex.z-dn.net/?f=%7B13%5Cchoose%205%7D%3D%5Cfrac%7B13%21%7D%7B5%21%5Ctimes%2813-5%29%21%7D%20%3D%5Cfrac%7B13%21%7D%7B13%21%5Ctimes8%21%7D%3D1287)
The number of ways of selecting 0 cards from 13 spades is:
![{13\choose 0}=\frac{13!}{0!\times(13-0)!} =\frac{13!}{13!}=1](https://tex.z-dn.net/?f=%7B13%5Cchoose%200%7D%3D%5Cfrac%7B13%21%7D%7B0%21%5Ctimes%2813-0%29%21%7D%20%3D%5Cfrac%7B13%21%7D%7B13%21%7D%3D1)
Compute the number of ways to select 5 diamonds and 3 clubs as:
![{13\choose0}\times{13\choose3}\times{13\choose5}\times{13\choose0} = 1\times286\times1287\times1=368082](https://tex.z-dn.net/?f=%7B13%5Cchoose0%7D%5Ctimes%7B13%5Cchoose3%7D%5Ctimes%7B13%5Cchoose5%7D%5Ctimes%7B13%5Cchoose0%7D%20%3D%201%5Ctimes286%5Ctimes1287%5Ctimes1%3D368082)
Thus, the number of ways to select 5 diamonds and 3 clubs is 368,082.
Answer:
4/15
Step-by-step explanation:
2x/5-3y/2=7
<em>Multiply all terms by the lcd.</em>
10(2x/5) + 10(-3y/2) = 10(7)
<em>Cross cancel.</em>
2(2x)+ 5(-3y) =70
<em>Simplify.</em>
4x -15y = 70
<em>Subtract 4x from both sides.</em>
-15y = -4x +70
<em>Divide by -15 on both sides.</em>
y= 4/15x -24/3
Answer:
41
Step-by-step explanation:
the sum of all 3 terms must equal 180 because triangles have 180 degrees. knowing this we can add all the terms together to get 4x+16=180. subtract 16 on both sides to isolate the variable and you get 4x=164 divide both sides by 4 to solve and you get 41
IM PRRETTY SURE ITS D BEB
Answer: a=3 & b=-2
Step-by-step explanation: