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

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. :)

20 minutes ago - 4

Update:

Nikolass, that is okay. I have done the same thing once before. I like the words you came up with so your time was not a total lost. Thanks though! LOL

3 Answers

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  • Andy J
    Lv 7
    1 decade ago
    Best answer

    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

  • 3 years ago

    those are all common permutation issues. to make certain what number mixtures could be made, you will possibly multiply the quantity of selections for the 1st place by potential of the quantity of ideas for the 2nd place, then multiply that by potential of the quantity of selections for the 0.33 place, and so on. yet be careful -- each and every so often using one for the 1st place facilitates you to no longer use it lower back for the 2nd place, as interior the 1st 3 ideas. you additionally can do this visually, by potential of making a tree diagram: draw all your ideas for the 1st place. Then by potential of one and all draw what can bypass after it. and so on. to illustrate, enable's do #a million: The scrabble tray has seven letters, and each could be used only as quickly as. you want a 4-letter affiliation, meaning there are 4 positions to be filled. so which you will possibly do 7x6x5x4, as a results of fact there are seven options for the 1st letter, and as quickly as a sort of is used you basically have 6 ideas for the 2nd, and so on. (in assessment to the registration quantity plate project, in which you have an identical quantity of selections for each letter area for the reason so which you are able to use a letter greater effective than as quickly as. so as that ought to be 26x26 for the letters, then x9x9x9 for the three digits) The seen technique might appear as if this: FERS FERX FERA FERI FESR FESX FESA FESI ...and so on. this might take continuously, besides the incontrovertible fact that it facilitates to do it once or twice so the mathematics version is wise.

  • 1 decade ago

    1. 6 letters

    ferias • fixers • fraise •

    5 letters

    Aesir • afire • AFISR • Aries • arise • fairs • fares • Farsi • faxes • fears • feria • fires • fixer • fixes • fries • raise • safer • Serax • serif • sixer •

    4 letters

    Rise • Fire • Sire • Airs • Fair • Fare • Fear • Arie • Firs • Safe • Sers ....Thats all i could find

    OMFG! I didn't read your question to the end! This is no use for you and i spent 20 minutes of my life! LOL

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