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6.Permutation and Combination
medium
There are $3$ sections in a question paper and each section contains $5$ questions. A candidate has to answer a total of $5$ questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is
A
$1500$
B
$2255$
C
$3000$
D
$2250$
(JEE MAIN-2020)
Solution
$\begin{array}{lll} \text { A } & \text { B } & \text { C } \\ \hline 5 & \text { 5 } & \text { 5 } \\ \text { 1 } & 2 & 2 \\ \text { 2 } & 1 & 2 \\ 2 & 2 & 1 \\ 1 & 1 & 3 \\ 1 & 3 & 1 \\ 3 & 1 & 1 \end{array}$
Total number of selection
$=\left({ }^{5} C _{1}{ }^{5} C _{2}{ }^{5} C _{2}\right) \cdot 3+\left({ }^{5} C _{1}{ }^{5} C _{1}{ }^{5} C _{3}\right) \cdot 3$
$=5 \cdot 10 \cdot 10 \cdot 3+5 \cdot 5 \cdot 10 \cdot 3$
$=2250$
Standard 11
Mathematics
