# Counting principles: 5 girls stand in a line. How many possible permutations...?

#### kuna

##### New member
1) 5 girls stand in a line. How many possible permutations are there in which Anya is at the left of the line or Elena is on the right, or both?

And the answer from my book is: 42

2) In how many ways can 5 different sweets be split amongst 2 people if one of the sweets is split into two to be shared, and each person gets two of the remaining sweets.

The answer to that is 12.

#### mmm4444bot

##### Super Moderator
Staff member
1) 5 girls stand in a line. How many possible permutations are there in which Anya is at the left of the line or Elena is on the right, or both?

2) In how many ways can 5 different sweets be split amongst 2 people if one of the sweets is split into two to be shared, and each person gets two of the remaining sweets.
What have you tried or thought about, so far? Where did you get stuck?

Do you know the meaning of "permutations"?

Have you tried listing some possibilities on paper, to look for a pattern?

For example, on the second exercise, if you write out a few combinations, you might realize a simplification. You can ignore the split sweet, at first. Figure out how many ways four different sweets can be split between two people. Once you have that number of combinations, think about the half sweets.

Please be sure that you have read the forum guidelines. Thanks! :cool: