GMAC 11th Edition Review Guide PS Question

I will take a stab at explaining this.

1. The original problem you had asked is about Permutation with repeating elements. The formula to solve those is Total number of permutations = N!/(K!*L!) where N is the number of items where K of the N elements are of the same type as well as L of the N elements are of the same type.

In your example: N = 5 (U,U,R,R,R)
K = 2 (U,U)
L=3 (R,R,R)

N!/(K!*L!) = 5!/(2!*3!) = 10

2. Removing second solution as I was thinking permutation and not combination

I hope this helps.

The two questions you are asking are different.

-How many different groups of 3 people can be formed from a group of 5 people?

This is a combination since the order in which 3 people are selected is NOT important. It is just the selection. Hence 5C3 is correct.

Applying the formula, nCk = n! / (r! * n-r!), we have 5! / (2! * 3!) = 10.

Now coming to the original question, there are 5 paths where 2 paths are upwards(U) and 3 paths are sideways(S).

To reach from source to distination, the order of the path is important. So this means it is Permutation.

Let me take an example - How many ways can we arrange PAGES. 5 distinct letters are there and order is important so it is 5!.
How many ways can we arrange FEELS - Again 5 words with a E repeated twice. It will be 5! / 2!.

Similary coming to our problem, UUEEE can be arranged in 5! / (2! * 3!) since U is repeated twice and E is repeated thrice.

https://regentsprep.org/regents/math/permut/LpermRep.htm

Google for Permutations with Repitions and you should find some information.

Oh ok great! Thanks a lot =)