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?

• A. $4$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is C $10$

Total no. of teacher$=50$

$n\left(TV\right)=22$

$n\left(VCR\right)=15$

$n\left(tape\right)=14$

$n(TV\bigcup VCR\bigcup Tape)$

$=22+15+14-$no. of teacher who own two of the items $-2$ no. of teachers who owns all the three

$=22+15+14-9-2\left(1\right)$

$=37+14-9-2$

$=51-11$

$=40$

No. of teachers who owns none of these

=total-no. of teachers who owns any of these

$=50-40$

$=10$