Dear experts:

Can someone please help me clarify the criteria to determine n and r in Permutations and combination. I think I am solving these problems by thumb rule rather on a proper understanding.

Below I have listed a few questions along with solutions where r is greater than n or i am not sure how allocate n ways to r blanks. Please help.

We know that the number of ways of filling up r blanks with n dissimilar things is nPr. The first blank can be filled with any one of the given n things in n ways.

Below I have a few examples:

Q1 In how many ways can 7 women go to 9 restaurants?

1 2 3 4 5 6 7 8 9

R blanks

N ways

The Permutation given is 97

Clarification: How do I determine which is n and which is r?

Q2 In an examination paper there are 8 questions each with 4 answer choices and 5 questions each with 2 answer choices. The no. of ways of answering the question if all the 13 questions are attempted is?

The Permutation given is 48 * 25

Clarification: How do I determine which is n and which is r?

Q3 In how many ways can 5 letters be posted in 6 boxes?

The Permutation given is 65

Clarification: How do I determine which is n and which is r?

Please help. Thank you

Determining-n-and-r.docx