7th Grade Math

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Lesson 1D Probability 447

15. OPEN ENDED Describe a real-world situation that has 6 permutations.


16. CHALLENGE There are 1,320 ways for three students to win first, second,
    and third place during a debate match. How many students are there on
    the debate team? Explain your reasoning.


17. E WRITE MATH The symbol P(10, 3) represents the number of
    permutations of 10 things taken 3 at a time. What does the symbol P(20, 4)
    represent? Explain how you would find P(20, 4).


18. SHORT RESPONSE The
    five finalists in a random
    drawing are shown. Find
    the probability that Sean
    is awarded first prize
    and Teresa is awarded
    second prize.


19. A baseball coach is deciding on the
    batting order for his nine starting
    players with the pitcher batting last.
    How many batting orders are
    possible?
    A. 8 C. 40,320
    B. 72 D. 362,880

An arrangement, or listing, of objects in which order is not important is

called a combination. You can find the number of combinations of objects by

dividing the number of permutations of the entire set by the number of ways

the smaller set can be arranged.

BASKETBALL A one-on-one basketball tournament has 6 players.

How many different pairings are there in the first round?

Find the number of ways 2 players can be chosen from a group of 6.

There are 6 · 5 ways to choose 2 people.

There are 2 · 1 ways to arrange 2 people.^

_^6 ×^5

2 × 1

= _^302 or 15

So, there 15 different pairings in the first round.

20. INTERNET Of 12 Web sites, in how many ways can you choose to visit 6?


21. TEAMS There are 8 members on the debate team. How many different
    5-player teams are possible?

C

Finalists

Cesar

Teresa

Sean

Nikita

Alfonso

440_447_C08_L1_895130.indd 447 12/29/09 1:18 PM