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Help me with these Combinations and Permutations problems?

1. How many 3 digits numbers, each less than 600, can be formed from the digits 8,6,4,2 if repetition of digits is allowed.

2.Your 14 friends include 3 married couples. How many ways can you invite 6 friends to dinner without breaking up any couples?

4 Answers

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  • Daniel
    Lv 7
    5 years ago

    The first answer is:

    show escoge [esmayor: 600] impon "junta multiconj clona list 3 [2 4 6 8]

    [222 224 226 228 242 244 246 248 262 264 266 268 282 284 286 288 422 424 426 428 442 444 446 448 462 464 466 468 482 484 486 488]

    show count escoge [esmayor: 600] impon "junta multiconj clona list 3 [2 4 6 8]

    32

  • 5 years ago

    1. Less than 600, so you're only allowed to use 4 and 2 for the first digit.

    You have 2 possibilities for the first digit.

    You have 4 possibilities for the second digit (because you're allowed to repeat)

    You have 4 possibilities for the third digit.

    3. So you have 6 friends who are in married couples and 8 who are not.

    You can invite no married couples: choosing 6 among the 8 singles is 8C6.

    You can invite one married couple: Choose 4 from among the 8 (8C4) and one from the three couples (3C1). Total of 8C4 * 3C1 ways to do this.

    You can invite two married couples: Choose 2 from among the 8 singles, and 2 from among the 3 couples.

    You can invite three married couples: Choose 3 from the 3 married couples.

    Add those up.

  • 5 years ago

    1. 2*4*4 = 32

    2. (8!/(6!*2!)) + (8!/(4!*4!))*3 + (8!/(2!*6!))*3 + 1 = 323

  • 5 years ago

    No

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