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Ray Of Light [21]
3 years ago
15

The 20 colleges of interest to a high school senior include 8 that are expensive ( tuition more than 20,000 per year), 8 that ar

e far from home( more than 200 miles away), and 7 that are both expensive and far from home. If the student decides to select a college that is not expensive and within 200 miles from home, how many selections are possible?
Mathematics
1 answer:
alekssr [168]3 years ago
7 0

Answer: 6

Step-by-step explanation:

Let  S= Total colleges

A = colleges are expensive.

B= colleges are  far from home( more than 200 miles away).

Given : n(S)= 20

n(A)=8

n(B)=8

n(A∩B) =2

Then, the number of  college that are not expensive and within 200 miles from home :-

n(A'\cap B')=n(S)-n(A\cup B)\\\\=20-(n(A)+n(B)-N(A\cap B))\ \ [\because\ n(A\cup B)=n(A)+n(B)-N(A\cap B)]\\\\=20-(8+8-2)\\\\=20-14=6

i.e.  the number of  college that are not expensive and within 200 miles from home=6

Hence, the number of possible selections are <u>6</u> .

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