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Permutations and Combination — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsPermutations and Combination1 Mark
Question
$30$ objects are to be divided into three groups containing $7, 10, 13$ objects. Find the number of distinct ways of doing so.
✓

Answer

First we can select $7$ objects out of $30$ for the first group in ${ }^{30} C _7$ ways.
Now there are $23$ objects left out of which we can select $10$ objects for the second group
in ${ }^{23} C _{10}$ ways.
Remaining $13$ objects can be selected for the third group in ${ }^5 C _5$ ways.
$\therefore$ Required number of ways $={ }^{30} C _7 \times{ }^{23} C _{10} \times{ }^{13} C _{13}$
$=\frac{30 !}{23 ! 7 !} \times \frac{23 !}{10 ! 13 !} \times 1$
$=\frac{30 !}{7 ! 10 ! 13 !}$

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