Different starting lineups can be created - 120+60+120=300. A certain college team has on its roster 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward.
1. A lineup without x is an example. You must decide.
- two of the three forwards;
- from 4 centers, 1 center.
It can be made as -
2C5 × 2C3× 1C4 = 10× 3×4 = 120 ways
2. Consider starting lineups with guard x. You must decide.
- 2 guards chosen from 6 quards (at least one of them must be x);
- two of the three forwards;
- from 4 centers, 1 center.
1C5×2C3×1C4 = 5×3×4 = 60 ways
3. Think about lineups where x is the forward. You must decide.
- 5 quards, 2 guards;
- 2 forwards from 4 forwards (x must be one of them);
- from 4 centers, 1 center.
2C5×1C3×1C4 = 10×3×4 = 120 ways.
Therefore, total number different lineups is - 120+60+120=300.
To learn more about combinations from given link
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Answer:
12
Step-by-step explanation:
30+(4x+2)=8+6x
30+4x+2=8+6x
32+4x=8+6x
32=8+6x-4x
32=8+2x
2x=32-8
2x=24
x=24/2
x=12
15:40
= 15/40
= 3:8
An equivalent to 15:40 is 3:8~
Collect like terms and calculate the sum
answer is: 4x+7
The correct proportion of the corresponding sides is 2 : 3
<h3>How to determine the proportion?</h3>
From the question, we understand that the shapes are similar.
This means that:
Ratio = GHIJ : KLMN
From the figure, we have:
GH = 6 and KL = 9
So, we have:
Ratio = 6 : 9
Simplify the ratio
Ratio = 2 : 3
Hence, the correct proportion of the corresponding sides is 2 : 3
Read more about similar shapes at:
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