Question

There are 44 candidates for a Natural Science Scholarship, 22 for a Classical and 66 for a Mathematical Scholarship, then find the number of ways in which these scholarships can be awarded is
(A) 66
(B) 110
(C) 63888
(D) 132

Answer 1

Hint: We start solving this problem by first finding the number of ways of awarding scholarships in each category, which is the number of ways of awarding Natural Science, Classical and Mathematical Scholarships. Then we find the total number of ways by multiplying the obtained values.

Complete step by step answer:
We are given that there are 44 candidates for a Natural Science Scholarship, 22 for a Classical and 66 for a Mathematical Scholarship.
We need to find the number of ways in which these scholarships can be awarded.
First, let us consider the number of ways in which a Nature Science Scholarship can be awarded.
As there are 44 candidates for a Natural Science Scholarship, we need to select one candidate for the scholarship.
We can select one candidate from 44 candidates in 44 ways.
Now let us consider the number of ways in which a Classical Scholarship can be awarded.
As there are 22 candidates for a Classical Scholarship, we need to select one candidate for the scholarship.
We can select one candidate from 22 candidates in 22 ways.
Now let us consider the number of ways in which a Mathematical Scholarship can be awarded.
As there are 66 candidates for a Mathematical Scholarship, we need to select one candidate for the scholarship.
We can select one candidate from 66 candidates in 66 ways.
So, we get the total number of ways in which the scholarship can be awarded as,
$\begin{align}
  & \Rightarrow 44\times 22\times 66 \\
 & \Rightarrow 63888 \\
\end{align}$
Hence, we get that the number of ways in which these scholarships can be awarded is equal to 63,888.
Hence answer is Option C.


Note:
 There is a possibility of one making a mistake while solving this question by finding the answer by adding the number of ways of awarding scholarships in each category, that is,
$\begin{align}
  & \Rightarrow 44+22+66 \\
 & \Rightarrow 132 \\
\end{align}$
One might solve like this and mark the answer as Option D. But it is wrong. As we are awarding scholarships in each category, we need to multiply the obtained values in each category. We will add them if only one scholarship is awarded out of all the categories.