How many ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary?
$1$ chair person and $1$ secretary can be selected from $10$ people in
${^{10}}{C}_{2} = \dfrac{10!}{8! \times 2!} = \dfrac{10 \times 9}{2} = 45$ ways.
Out of the remaining $8$ people, $4$ people can be selected in
${^{8}}{C}_{4} = \dfrac{8!}{4! \times 4!}= \dfrac{8 \times 7 \times 6 \times 5 \times 4!}{4! \times 4!} = \dfrac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70$ ways
$\therefore \;$ Number of ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary $= 45 \times 70 = 3150$ ways