A scrabble tray contains the tiles FERSXAI. How many different four-letter arrangements can be made?

Letter Tray

andyjalc asks:

1. A scrabble tray contains the tiles FERSXAI. How many different four-letter arrangements can be made?

2. In how many ways can a committee of two boys and three girls be formed from a group of 10 boys and 12 girls?

3. How many different ways can three chocolate, four strawberry, and two butterscotch sundaes be served to nine people?

4. An auto license plate is made using two letters followed by three digits. How many license plates are possible?

This is for pre calc and I am puzzled by what to do as I have tried them all, but the answers I got don’t match up. Someone please help me and thanky you so much in advance. 🙂

Best answer:

Answer by AndyJ
1. Order is important, so we use permutations. Since there are no repeated letters, the answer is simply 7P4 = 840

2. 10C2 * 12C3 = 45 * 220 = 9900

3. Assuming every person gets exactly one sundae. We simply need to find the permutation of the 9 sundaes. Normally this is 9!, but with repeats, we need to divide out the indistinguishable permutations of the 3, 4 and 2 identical sundaes. The answer is thus:

9! / (3!4!2!) = 1260

4. 26 * 26 * 10 * 10 * 10 = 676000

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