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  • Six have to be placed in the squares of Fig. 6.2 such that each row contain at least one <img alt="\m

Six \mathrm{X} have to be placed in the squares of Fig. 6.2 such that each row contain at least one \mathrm{X}. The number of ways in which this can be done is

Option: 1

25


Option: 2

27


Option: 3

226


Option: 4

30


Answers (1)

best_answer

This can be done in four mutually exclusive ways as follows:

\begin{tabular}{|l|c|c|c|l|} \hline & $\begin{array}{l}\text { Row } \\ R_{1}\end{array}$ & Row $R_{2}$ & Row $R_{3}$ & Number of ways \\ \hline I & 1 & 3 & 2 & $\left({ }^{2} C_{1}\right)\left({ }^{4} C_{3}\right)\left({ }^{2} C_{2}\right)=8$ \\ \hline II & 1 & 4 & 1 & $\left({ }^{2} C_{1}\right)\left({ }^{4} C_{4}\right)\left({ }^{2} C_{1}\right)=4$ \\ \hline III & 2 & 2 & 2 & $\left({ }^{2} C_{2}\right)\left({ }^{4} C_{2}\right)\left({ }^{2} C_{2}\right)=6$ \\ \hline IV & 2 & 3 & 1 & $\left({ }^{2} C_{2}\right)\left({ }^{4} C_{3}\right)\left({ }^{2} C_{1}\right)=8$ \\ \hline & & & Total & 26 \\ \hline \end{tabular}

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