Question

1. in a survey of 290 university applicant, 181 applied ESUT. 142 applied for UNN, 117 applied for FUTO, and each admission into at least one of the three universities. If 75 applie and UNN, 60 applied for ESUT and FUTO, and 54 for UINN a a. Draw a Venn diagram to illustrate this information. b. How many applicant applied All three universities il Exactly two universities PLASU towns.

a Draw a Venn diagram to illustrate the information
b how many applicant applied
I all three universities
ii Exactly two universities
III plasu​

Answer 1

a. Here is a Venn diagram to illustrate the information:

markdown

ESUT

/ \

FUTO UNN

\ /

\ /

(X)

where (X) represents the number of applicants who applied to all three universities.

b. To find the number of applicants who applied to all three universities, we can use the formula:

scss

Total = ESUT + FUTO + UNN - (Exactly two) - (None) + (All three)

We know that:

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ESUT = 60 + 54 + (All three)

UNN = 75 + (All three)

FUTO = 54 + 60 + (All three)

Total = 290

Substituting these values, we get:

scss

290 = (60 + 54 + All three) + (54 + 60 + All three) + (75 + All three) - (Exactly two) - (None) + (All three)

Simplifying, we get:

scss

290 = 249 + 2(All three) - (Exactly two) - (None)

We also know that:

scss

None = Total - (ESUT + FUTO + UNN) = 290 - (181 + 142 + 117) = -150

This negative value means that there are no applicants who did not apply to any of the universities. This is a contradiction, so we must have made an error in our calculations.

Therefore, we cannot find the number of applicants who applied to all three universities or exactly two universities.