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Colt1911 [192]
3 years ago
6

A baseball team has 15 field players and 10 pitchers. Each field player can take any of the 8 non-pitching positions. What is th

e number of possible starting lineup (8 field player 1 pitcher)
Mathematics
1 answer:
leonid [27]3 years ago
7 0

Answer:

If order matters: 2,594,592,000 ways.

If order does not matter:  64,350 ways

Step-by-step explanation:

Assuming that the order matters when picking the non-pitching positions (since they are different positions), the number of possible different starting lineups is given by the permutation of picking 8 players out of 15, multiplied by 10 (pick one out of 10 pitchers):

n =10*\frac{15!}{(15-8)!}\\ n=10*15*14*13*12*11*10*9*8\\n=2,594,592,000

Now if the order of the field players is not important, the number of possible starting lineups is given by the combination of picking 8 players out 15, multiplied by 10:

n = n =10*\frac{15!}{(15-8)!8!}\\ n=\frac{10*15*14*13*12*11*10*9*8}{8*7*6*5*4*3*2} \\n=64,350

Therefore, the number of ways to pick the starting lineup is:

If order matters: 2,594,592,000 ways.

If order does not matter:  64,350 ways

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Answers:

  • <u>24000 dollars</u> invested at 4%
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======================================================

Work Shown:

x = amount invested at 4%

If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%

She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account

This means we have

0.04x+0.07(42000-x)

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This represents the total amount of money earned after 1 year.

We're told the amount earned in interest is $2220, so we can say,

-0.03x+2940 = 2220

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x = -720/(-0.03)

x = 24000 dollars is the amount invested at 4%

42000-x = 42000-24000 = 18000 dollars was invested at 7%

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As a check, we can see that

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and also

0.04x = 0.04*24000 = 960 earned from the first account

0.07*18000 = 1260 earned from the second account

1260+960 = 2220 is the total interest earned from both accounts combined

This confirms our answers.

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Answer:

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Step-by-step explanation:

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