Question
Match each item given under the column $C_1$ to its correct answer given under the column $C_2.$
There are $10$ professors and $20$ lecturers out of whom a committee of $2$ professors and $3$ lecturer is to be formed. Find:
There are $10$ professors and $20$ lecturers out of whom a committee of $2$ professors and $3$ lecturer is to be formed. Find:
|
|
$C_1$
|
$C_2$ | |
| $(a)$ |
In how many ways committee can be formed.
|
$(i)$ | $^{10}C_2 \times ^{19}C_3$ |
| $(b)$ |
In how many ways a particular professor is included.
|
$(ii)$ | $^{10}C_2 \times ^{19}C_2$ |
| $(c)$ |
In how many ways a particular lecturer is included.
|
$(iii)$ | $^9C_1 \times ^{20}C_3$ |
| $(d)$ |
In how many ways a particular lecturer is excluded.
|
$(iv)$ | $^{10}C_2\times ^{20}C_3$ |