FCP and Permutation

Describe the Type of Problem:

Ben has to pick 2 kittens from a litter of 4.

• Combination

• Permutation

• Fundamental Counting Principle

How many ways can the 7 Harry Potter books be arranged on a shelf? Which is/are not a correct answer to the problem?

How many permutations are there in the letters of the word FROZEN?

Answer explanation

There are 6 different letters, so the permutation is solved using nPn=6!. 6!=6x5x4x3x2x1=720

You have 12 books stacked up on a table. How many ways can they be stacked if 3 of these books have to be together? (Read carefully and understand the problem.)

In how many ways can four men and three women arrange themselves in a row for picture taking if the men and women must stand in alternate positions? (Take note that the number of men and women is not the same)

Answer explanation

4x3x3x2x2x1x1

Seven bands have volunteered to perform at a benefit concert, but there is only enough time for four of the bands to play. How many lineups are possible?

For a segment of a radio show, a disc jockey (Dr. Jams) can play 4 songs. If there are 8 to select from, in how many ways can the program for this segment be arranged?

Six people will sit in a row, but out of them, Ronnie, will always be left of Annie and Rachel will always be right of Annie. How many row arrangements are possible?

Ten students have appeared for a test in which the top three will get a prize. How many possible ways are there to get the prize winners?

In how many ways can 3 different vases be arranged on a tray?
 

• 3

• 9

• 6

• 12