Respuesta :
Answer:
100 students play only basketball.
Step-by-step explanation:
We are given the following information in the question:
Total number of students in school = 240
Number of students that play soccer =
[tex]\dfrac{1}{3}\times \text{Total number of students}\\\\=\dfrac{1}{3}\times 240 = 80[/tex]
n(S) =80
[tex]n(S\cap B) = 44[/tex]
[tex]n(S'\cap B') = 60[/tex]
Formula:
[tex]n(S\cup B) = \text{Total} - n(S' \cap B')\\n(S\cup B) = n(S) + n(B) - n(S\cap B)[/tex]
Putting the values, we get,
[tex]n(S\cup B) =240-60=180\\n(S\cup B) = 180 = 80 - 44 + n(B)\\n(B) = 180 - 80 + 44= 144[/tex]
Thus, 144 students play basketball.
Out of these 144, 44 plays soccer as well.
[tex]\text{Student only playing basketball} = 144 -44 = 100[/tex]
Thus, 100 students play only basketball and not soccer.
