Question 9 and 10, Exercise 6.3

Solutions of Question 9 and 10 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find the number of diagonals in $n$ sided polygon?

Solution.

$n$-sided polygon is determined by $n$-points
and all possible lines between $n$ points is $C_{2}$
but $n$ lines are sides of polygon and rest are diagonals.
So number of diagonals of $n$-sided polygon $={ }^{n} C_{2}-n$
or $=\frac{n!}{2!(n-2)!}-n$

In how many ways a group of $10$ girls can be diided into two groups of $10$ and $3$ girls?

Solution.

$7$ girls can be chosen out $10$ in ${ }^{10} C_{7}$ ways had after choosing
these $7$ girls remaining $3$ girls can be chosen in only one way. So
Total number of ways to divide girls into two groups of 3 and $7={ }^{10} C_{7}=120$

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