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

To find the number of ways to select seven members from the 78-member Puerto Rican legislature, we use the combination formula. The order of selection does not matter, so the combination formula is C(78, 7) which equals 78! / (7!71!).

Step-by-step explanation:

To determine how many ways there are to choose a group of seven members from the Puerto Rican legislature, we apply the concept of combinations in mathematics. The Puerto Rican legislature consists of a 27-member Senate and a 51-member House of Representatives, totaling 78 members. When selecting a group of seven members from this total, the order does not matter, so we use the combination formula:

C(n, k) = n! / (k!(n - k)!)

Here, 'n' represents the total number of items, and 'k' represents the number of items to choose. Applying this to our case:

C(78, 7) = 78! / (7!(78 - 7)!) = 78! / (7!71!)

Calculation of this using factorial reduction leads to the final answer, which represents the number of different groups of seven that can be formed from the entire legislature.

This combinatorial problem falls within the topic of binomial coefficients and probability, which are taught in advanced high school mathematics classes.

Answer 2

There can be 8. A senator will be S and a representative will be R: you have: SSSSSSS SSSSSSR SSSSSRR SSSSRRR SSSRRRR SSRRRRR SRRRRRR RRRRRRR