# There Are 10 Professors and 20 Students Out of Whom a Committee of 2 Professors and 3 Students is to Be Formed.A Particular Student is Excluded. - Mathematics

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:

a particular student is excluded.

#### Solution

Clearly, 2 professors and 3 students are selected out of 10 professors and 20 students, respectively.
Required number of ways  =${}^{10} C_2 \times^{20} C_3 = \frac{10}{2} \times \frac{9}{1} \times \frac{20}{3} \times \frac{19}{2} \times \frac{18}{1} = 51300$

If a particular student is excluded, it means that 3 students are selected out of the remaining 19 students.
Required number of ways =${}^{19} C_3 \times^{10} C_2 = \frac{19}{3} \times \frac{18}{2} \times \frac{17}{1} \times \frac{10}{2} \times \frac{9}{1} = 43605$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 5.3 | Page 15