Question

The legislature of Puerto Rico consists of a 27-member Senate and a 51-member House of Representatives.

How many ways are there to choose a group of seven members from the Puerto Rican legislature?

Answer 1

@Hunus

Answer 2

@satellite73

Answer 3

hello honey, your question is ambiguous since there is no rule to choose members.

Answer 4

This is the complete question ma'am ..

Answer 5

ok, got it, let me tag someone else @e.mccormick

Answer 6

thanks :)

Answer 7

I mean: among of 7 members, what is the ratio of Senators and Representatives

Answer 8

Legislature
The Legislative Power resides in the Senate and in the Chamber of Representatives. The Senate consists of 27 members, 2 per electoral district, and 11 elected according to the different districts proportion of population. Two extra seats are granted in each house to the opposition if necessary to limit any party's control to two thirds.

Answer 9

In the house or senate does not matter for the math, so it is a pool of both and picking 7 at random without replacement.

Answer 10

ok, go ahead, friend, I don't understand a word. hihih..

Answer 11

Have you been studying permiutations?

Answer 12

yes..

Answer 13

Seen the formula for combinations where order does not matter and repetition is not allowed?

Answer 14

i dont recall..

Answer 15

\[\frac{n!}{r!(n-r)!}\]That spark any memories?

Answer 16

sure! :)

Answer 17

Got it from there?

Answer 18

no :(

Answer 19

Well, do you know what the ! means?

Answer 20

Factorials:
\[5! = 5\cdot 4\cdot 3\cdot 2\cdot 1\]

Answer 21

ok got that

Answer 22

If n is the number of items in the pool and your order of selection is not important, but there is not replacement, then the when you choose r items from the pool the possible combinations is given by:
\[\frac{n!}{r!(n-r)!}\]

Answer 23

So, what is your total pool size here (n)? ANd how many will you choose from it (r)?

Answer 24

n=51+27 and r = 7?

Answer 25

Yes. So put those in as 78 and 7, then solve.

Answer 26

ok thx

Answer 27

So, what did you get?

Answer 28

78*76*75 and so on?

Answer 29

Well, there is a lot of reduction. The 71 on the bottom nocks out most of it and the 7 nocks out a little more.

Answer 30

\[\frac{78!}{7!(78-7)!}\implies \frac{78!}{7!(71)!}\]See, the 71 on the bottom automatically kills from 71 down to 1. Do you understand what I mean by that?

Answer 31

As an example with smaller numbers:
\[\frac{8!}{6!}\implies \frac{8 \cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}\implies \\
\frac{8 \cdot 7\cdot \not6\cdot \not5\cdot \not4\cdot \not3\cdot \not2\cdot \not1}{\not6\cdot \not5\cdot \not4\cdot \not3\cdot \not2\cdot \not1}\implies \\
8\cdot 7 = 56\]

Answer 32

ok i need pen n paper.. i will get back to u tomm. thx

Answer 33

OK... well. I did it in a text file. LOL. But you can see how the 71! makes it a lot simpler. The 7! will help some too. Then you just need to multiply what is left.

Answer 34

so the answer would be 78times76times75times74times73times72?

Answer 35

1.3315187e+13 that does seem right

Answer 36

@malia667 honey, I do not follow the steps e.mccormick gave you, but I trust him. you can take it. (sorry for the message I sent you that said "yes , it is" without checking the stuff)

Answer 37

@e.mccormick

Answer 38

Well you are choosing 7 people out of 78. C(78,7). Either use the calculator or apply the formula

Answer 39

Did you remember to also cancel out the 7! part? You are high, and that might do it.

Answer 40

so what do i multiply?

Answer 41

Because the 71! cancels, you are left simplifying this:\[\frac{78!}{7!71!}\implies \frac{78\cdot 77\cdot 76\cdot 75\cdot 74\cdot 73\cdot 72 }{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2}\]