An organization awarded 48 medals in event A, | vedclass

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

Question

(C) Let $|A|=48$,$|B|=25$,and $|C|=18$. Given the total number of men who received at least one medal is $|A \cup B \cup C|=60$. Given the number of m

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(C) Let $|A|=48$,$|B|=25$,and $|C|=18$. Given the total number of men who received at least one medal is $|A \cup B \cup C|=60$. Given the number of men who received medals in all three events is $|A \cap B \cap C|=5$. Using the principle of inclusion-exclusion: $|A \cup B \cup C| = (|A| + |B| + |C|) - (|A \cap B| + |B \cap C| + |C \cap A|) + |A \cap B \cap C|$. Let $S_1 = |A| + |B| + |C| = 48 + 25 + 18 = 91$. Let $S_2 = |A \cap B| + |B \cap C| + |C \cap A|$. Then $60 = 91 - S_2 + 5$. $S_2 = 91 + 5 - 60 = 36$. The number of men who received medals in exactly two events is given by the formula: $N(	ext{exactly two}) = S_2 - 3|A \cap B \cap C|$. $N(	ext{exactly two}) = 36 - 3(5) = 36 - 15 = 21$.

An organization awarded $48$ medals in event $A$,$25$ in event $B$,and $18$ in event $C$. If these medals were awarded to a total of $60$ men and only $5$ men received medals in all three events,how many men received medals in exactly two of the three events?

Similar Questions

If sets $A$ and $B$ have $3$ and $6$ elements respectively,what is the minimum number of elements in $A \cup B$?

In a certain school,$74 \%$ of students like cricket,$76 \%$ of students like football,and $82 \%$ of students like tennis. Then,all three sports are liked by at least $...... \%$ of students.

Let $S = \{1, 2, 3, \ldots, 2022\}$. The probability that a randomly chosen number $n$ from the set $S$ satisfies $\operatorname{HCF}(n, 2022) = 1$ is:

Let $A = \{1, 6, 11, 16, \dots\}$ and $B = \{9, 16, 23, 30, \dots\}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A \cup B)$ is

If a set $A$ is such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$,then the set $A$ could be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module