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Standard XII
Maths
Question

Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorders; and, one college teacher owns all three, how many of the 50 college teachers own none of three, colour TV, VCR or tape recorder?
  1. 4
  2. 9
  3. 10
  4. 11

A
10
B
11
C
4
D
9
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Solution
Verified by Toppr

Total no. of teacher=50
n(TV)=22
n(VCR)=15
n(tape)=14
n(TV⋃VCR⋃Tape)
=22+15+14−no. of teacher who own two of the items −2 no. of teachers who owns all the three
=22+15+14−9−2(1)
=37+14−9−2
=51−11
=40
No. of teachers who owns none of these
=total-no. of teachers who owns any of these
=50−40
=10

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