Question
Match each item given under the column C1 to its correct answer given under the column C2.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
C1
C2
(a)
In how many ways committee can be formed.
(i)
10C2 × 19C3
(b)
In how many ways a particular professor is included.
(ii)
10C2 × 19C2
(c)
In how many ways a particular lecturer is included.
(iii)
9C1 × 20C3
(d)
In how many ways a particular lecturer is excluded.
(iv)
10C2 × 20C3

Answer

C1
C2
(a)
In how many ways committee can be formed.
(iv)
10C2 × 20C3
(b)
In how many ways a particular professor is included.
(iii)
9C1 × 20C3
(c)
In how many ways a particular lecturer is included.
(ii)
10C2 × 19C2
(d) In how many ways a particular lecturer is excluded. (i) 10C2 × 19C3
Explanation:
  1. We have to select 2 professor out of 10 and 3 lecturers out of 20 $\therefore$ Number of ways of selection = 10C2 × 20C3
  2. When a paeticular professor is included the number of ways = 10 - 1C1 × 20C3 = 9C1 × 20C3
  3. When a particular lecturer is included number of ways = 10C2 × 19C2
  4. Whan a particular lecturer is excluded, then number of ways = 10C2 × 19C3

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $\sin\text{x}=\frac{12}{13}$ and x lies in the second quadrant, find the value of $\sec\text{x}+\tan\text{x}.$
Five cards are drawn from form a pack of 52 cards. what is the chance that these 5 will contain:
  1. Just one ace
  2. At least one ace.
Solve the following equations:
$\sin\text{x}\ \tan\text{x}-1\tan\text{x}-\sin\text{x}$
A person observes the angle of elevation of the peak of a hill from a station to be $\alpha.$ He walks c metres along a slope inclined at an angle $\beta$ and finds the angle of elevation of the peak of the hill to be $\gamma.$ Show that the height of the peak above the ground is $\frac{\text{c}\sin\alpha\sin(\gamma-\beta)}{(\sin\gamma-\alpha)}.$
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{3}{2}}-(\text{a}+2)^{\frac{3}{2}}}{\text{x}-\text{a}}$
Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$\frac{\text{f}}{\text{g}}$
Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipse:
$5\text{x}^2+4\text{y}^2=1$
Solve the following systems of linear inequations graphically:
$2\text{x}+3\text{y}\leq6,\text{x}+4\text{y}\leq4,\text{x}\geq0,\text{y}\geq0$
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{1-\cos2\text{x}}{\cos2\text{x}-\cos8\text{x}}$
Evaluate the following limit:
Evaluate: $\lim\limits_{\text{n}\rightarrow\infty}\frac{1^4+2^4+3^4+\ \cdots+\text{n}^4}{\text{n}^5}-\lim\limits_{\text{n}\rightarrow\infty}\frac{1^3+2^3+\ \cdots+\text{n}^3}{\text{n}^5}$