Question

in a University out of 120 students 15 opted mathematics only,16 opted statistics only,9 opted for physics only 45 objective Physics and Mathematics, 30 opted physics and Statistic,8 opted mathematics and statistics and 80 opted a Physics find the number of students who
1) opted mathematics
2) opted statistics
3) did not opted any of the above three subjects​

Answer 1

Answer:

1) students opted mathematics=64

2) students opted statistics=50

3) students did not opted for any=5

Step-by-step explanation:

Let studens opted for physics is P=80

Let n(M∩P∩S) =x n(M∩P) =45 n(P∩S) =30 n(S∩M) =8

physics, 80-(45-x+x+30-x) =9 solving we get x=n(M∩P∩S)=4,

1) opted for mathematics

M-(41+4+4) =15 solvingM=64

2) opted for statistics

S-(26+4+4) =16 solving S=50

3) not opted for any =Y

n(MUPUS) =n(M) +n(S) +n(P) -n(M∩P)-n(P∩S)-n(M∩S)+n(M∩P∩S)=64+50+80-45-30-8+4=115

Y=total-n(MUPUS)=120-115=5