In a school of 800 boys,224 play cricket,240 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $C$,$H$,and $B$ represent the sets of boys who play cricket,hockey,and basketball,respectively.Given:$n(U) = 800$$n(C) = 224, n(H) = 240, n(B)

Vedclass · Accepted Answer

$160$

Vedclass · Answer

(D) Let $C$,$H$,and $B$ represent the sets of boys who play cricket,hockey,and basketball,respectively.Given:$n(U) = 800$$n(C) = 224, n(H) = 240, n(B) = 336$$n(B \cap H) = 64, n(C \cap B) = 80, n(C \cap H) = 40$$n(C \cap H \cap B) = 24$Using the Principle of Inclusion-Exclusion:$n(C \cup H \cup B) = n(C) + n(H) + n(B) - [n(C \cap H) + n(H \cap B) + n(C \cap B)] + n(C \cap H \cap B)$$n(C \cup H \cup B) = 224 + 240 + 336 - [40 + 64 + 80] + 24$$n(C \cup H \cup B) = 800 - 184 + 24 = 640$The number of boys who do not play any game is $n(U) - n(C \cup H \cup B) = 800 - 640 = 160$.

In a school of $800$ boys,$224$ play cricket,$240$ play hockey,and $336$ play basketball. Of the total,$64$ play basketball and hockey,$80$ play cricket and basketball,and $40$ play cricket and hockey,while $24$ play all three games. Find the number of boys who do not play any game.

Similar Questions

If a number is chosen at random from the first $200$ positive integers,what is the probability that it is divisible by $6$ or $8$?

The sum of all the elements in the set $\{n \in \{1, 2, \ldots, 100\} \mid \text{H.C.F. of } n \text{ and } 2040 \text{ is } 1\}$ is equal to $.....$

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments,then $K$ cannot belong to the set :

Let $S = \{1, 2, 3, 4, 5, 6, 9\}$. Then the number of elements in the set $T = \{A \subseteq S : A \neq \phi \text{ and the sum of all the elements of } A \text{ is not a multiple of } 3\}$ is ..... .

In a group of students,$100$ students know Hindi,$50$ know English,and $25$ know both. Each student knows either Hindi or English. How many students are there in the group?

Vedclass Test Series

Exam Paper Generator

Online Exam Module