locmsimon asked in 科學及數學數學 · 9 years ago

# 數學題(Combination)#10 15分

ans:7a=20 b=10 c=70 8a=5 b=25 10a=9 b=6

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• ?
Lv 7
9 years ago

7(a) As Blue Jays needs to win until 7 games,

then the result of first six games should be 3-3

So, no. of ways = C(6,3) = 20

(b) As Expos needs to win until 6 games

then the result of first five games should be 3-2

So, no. of ways = C(5,3) = 10

(c) Consider Blue Jays

Wins in 4 games, 1 ways

Wins in 5 games, 4 ways

Wins in6 games, 10 ways (result of (b))

Wins in 7 games 20 ways (result of (a))

Total 35 ways

Similarly for Expos

Total possible ways = 2 * 35 = 70

10(a) 3 * 3 = 9 routes

(b) 3 * 2 = 6 routes (As a man cannot use the rural roads for return)

• ?
Lv 5
9 years ago

7a.

BJ should win the 7th game

so only first 6 games will be consider in the series

BJ should win 3 out of 6 games to get 7th game

the combination is 6C3 = 20

7b.

EX should win the 6th game

so only first 5 games will be consider in the series

EX should win 3 out of 5 games to get 7th game

the combination is 5C3 = 10

7c.

(consider BJ wins the series means BJ wins the lastmost game and so the games to be considered should be minus 1)

in 4 games = 3C0 = 1

in 5 games = 4C1 = 4

in 6 games = 5C2 = 10

in 7 games = 6C3 = 20

as there are 2 teams, so the total combination of series = 2x(1+4+10+20)

= 70

8. (what is the question?)

10a.

routes from A to B = 3

routes from B to A = 3

so total routes from A to B and back to A = 3x3 = 9

10b.

routes from B to A = 2

so total routes from A to B and back to A = 3x2 = 6

2011-12-16 22:59:53 補充：

7a.

the 7th game will play only when each team wins 3 games

7c.

e.g. BJ wins the series in 5 games

4 possible ways and you can realize BJ will get the last match:

EX-BJ-BJ-BJ-BJ

BJ-EX-BJ-BJ-BJ

BJ-BJ-EX-BJ-BJ

BJ-BJ-BJ-EX-BJ