Permutation and combination?

A bag contains six white marbles and five red marbles. Find the number

of ways four marbles can be drawn from the bag if

(i) they can be any color.

(ii) two must be white and two red.

(iii) they must all be of the same color.

3 Answers

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  • David
    Lv 7
    8 years ago
    Favorite Answer

    there are 6 + 5 = 11 marbles

    11C4 = 330

    6C2 * 5C2 =

    15 * 10 = 150

    6C4 + 5C4 =

    15 + 5 = 20

  • dymke
    Lv 4
    4 years ago

    permit her elect the ribbons one via one. For the 1st one, she has 6 thoughts. For the 2d, there are 5 thoughts left. So there are 30 distinctive procedures of choosing an ordered pair of ribbons. whether, Cathy would not care relating to the order. Taking first a blue and then a white ribbon is the comparable as taking a white ribbon first and then a blue one. this skill we counted double the kind of opportunities. So the extremely quantity is 5*6 / 2 = 15. this is, in result, a mix: 2C6. The reasoning at the back of the formulation for mixtures is as follows: you could placed all six ribbons in 6! distinctive orderings. Of the six taken care of ribbons you could then elect the 1st 2. As you do no longer care relating to the order of those 2, you could divide the quantity via the kind of procedures of ordering those 2: 2!. the comparable is going for the 4 ribbons Cathy did no longer elect: those may be in 4! distinctive orderings. So the finished kind of available mixtures is 6! / (2! 4!)

  • 8 years ago

    1. 11C4

    2. 6C2 x 5C2

    3. 5C4 + 6C4

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