Out of 800 boys in a school,224 played cricke | vedclass

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

Question

(D) Let $C, H, B$ represent the sets of boys who play cricket,hockey,and basketball,respectively.Given: $n(C) = 224, n(H) = 240, n(B) = 336$.Intersect

Vedclass · Accepted Answer

$160$

Vedclass · Answer

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

Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey. $24$ played all three games. The number of boys who did not play any game is:

Similar Questions

$X, Y, Z$ are the sets of all positive divisors of $10^{60}, 20^{50},$ and $30^{40}$ respectively. Find $n(X \cup Y \cup Z)$.

In a survey,it was found that $63\%$ of Americans like cheese and $76\%$ like apples. If $x\%$ of Americans like both cheese and apples,then:

The number of integers from $1$ to $1000$ which are divisible by $2$ or $3$ is

$A$ number is chosen at random from the set $\{1, 2, 3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$. Then the value of $500p$ is . . . . . .

Let $A = \{n \in N \mid n^{2} \leq n + 10,000\}$,$B = \{3k + 1 \mid k \in N\}$,and $C = \{2k \mid k \in N\}$. Then the sum of all the elements of the set $A \cap (B - C)$ is equal to $.....$

Vedclass Test Series

Exam Paper Generator

Online Exam Module