Match the following.

Question 14 Marks

There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturers is to be formed. Find :

(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) ${ }^{9} C_1 \times{ }^{20} C_3$
(d) In how many ways a particular lecturer is excluded	(i) ${ }^{10} C_2 \times{ }^{20} C_3$

Answer

(a) ↔ (iv), (b) ↔ (iii), (c) ↔ (ii), (d) ↔ (i).

Question 24 Marks

Five boys and five girls form a line. Find the number of ways of making seating arrangements under the following conditions :

$C _1$	$C _2$
(a) Boys and girls alternate	(i) $5!\times 6$ !
(b) No two girls sit together	(ii) $10!-5! 6$ !
(c) All the girls sit together	(iii) $(5!)^2+(5!)^2$
(d) All the girls are never together	(iv) $5!\times 6$ !

Answer

(a) ↔ (iii), (b) ↔ (i), (c) ↔ (iv), (d) ↔ (ii)

Applied Maths Match the following.