Question

in a class of 50 students, 35 students like to play football and 40 students like to play cricket, all the students play one of the games. find how many students like to play only cricket​

Answer 1

Step-by-step explanation:

we need to find the number of students who play only cricket.

\large\bf\underline{Given:-}

Given:−

Total number of students = 50

35 students play's football

25 students play cricket as well as football.

\huge\bf\underline{Solution:-}

Solution:−

Let F denotes the set of people who plays football and C denotes the set of people who plays cricket.

So,

n(F ∪ C) = 50

n(F) = 35

n(F ∩ C) = 25

we know that,

\purple{ \underline{ \boxed{ \rm \: n(F \cap \: C) + n(F \cup \: C) = n(F) + n(C)}}}

n(F∩C)+n(F∪C)=n(F)+n(C)

n(F ∩ C) + n( F ∪ C) - n(F) = n(C)

➛ 25 + 50 - 35 = n(C)

➛ 75 - 35 = n(C)

➛ 40 = n(C)

so,

40 students plays cricket

Finding number of students who only plays cricket.

➛ n(C) = n(C ∩ F) + n(C - F)

➛ 40 = 25 + n(C - F)

➛ 40 - 25 = n(C - F)

➛ 15 = n(C - F)

➛ n(C - F) = 15

hence,

⚘ 15 students plays only cricket

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Answer 2

Step-by-step explanation:

5 students play another game