Question

1. ind the number of ways of selecting 12 balls from 6 red bal

   COMBINATION

   Solve each of the following problems. (Show your work.)

2. Find the number of ways of selecting 12 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 4 balls of each color.
3. Among the seven nominees for two vacancies on the city council are four men and six

4.            women. In how many ways may these vacancies be filled

                 a). with any two of the nominees?

                 b). with any two of the women?

                 c). with one of the men and one of the women?

5. A test consists of 25 questions, but you are told to answer only 15. In how many different ways can you choose the 15 questions?
6. Twenty points are taken on the circumference of a circle. With these 20 points as vertices, how many triangles can be drawn?
7. The vertices of a polygon determine 56 triangles. How many sides does the polygon have?
8. A committee of 7 is to be formed out of 6 gents and 4 Ladies. In how many ways this can be done, when

9.                a). at least two ladies are included?                            b). at most two ladies are included?

10. From a class of 10 students, 6 girls and 4 boys, how many committees of 5 students can be selected if there:

11. a). are no further restrictions?                                  b). must be at least 1 girl?

    c). must be a particular boy chosen?                       d). must be more boys than girls?

    e).   must be at most 2 girls only?   

12. From a class of 25 students 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can excursion party be chosen?
13. Two balls are drawn without replacement from an urn with 5 red, 3 white, 6 blue balls. Find the number of ways for selecting two balls:

14. a). with the same color                                         b). with different colors

    c). 1 red, 1 white                                                  d). red or white

15. Given a deck of 52 cards, if 5 cards are selected:

16. a). how many different five-card hands are possible?

    b). in how many hands are all five cards the same color?

    c). in how many hands are all five cards the same suit?

    d). four face cards and one that is not a face card?

    e). three queens and two that are not queens?

    f). full house (three of a kind, two of a different kind)?

    g). royal flush (10, J, Q, K and ace of the same suit)?

    h). at least one heart?

    i). at least one ace?

    j). at most two spades?

17.   A college football team plays 10 games during the season. In how many ways can it end the

18.               season with 5 wins, 4 losses, and 1 tie?

19. If seven people eat dinner together, in how many different ways may 3 order chicken, 2 order

20.              steak, and 2 order lobster?

21. Suppose a True-False test has 10 questions.

22.              a). In how many ways may a student mark the test, if each question is answered?

                 b). In how many ways may a student mark the test, if 7 questions are marked correctly and

                       3 incorrectly?

               c). In how many ways may a student mark the test, if 5 questions are marked correctly

                       and 5 incorrectly?

    ls, 5 white balls and 5 blue balls if each selection consists of 4 balls of each color.

Answer 1

Find the number of ways of selecting 12 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 4 balls of each color.

Number of ways of selecting 4 red balls, 4 white balls and 4 blue balls is

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Since there are 4 men and 6 women so total number of nominees are 4+6 = 10.

(a)

Number of ways of selecting 2 nominees are

(b)

Number of ways of selecting 2 women out of 6 is

(c)

Number of ways of selecting 1 man and 1 woman out of 6 is