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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 Included. - 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 included.

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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 included, it means that 2 students are selected out of the remaining 19 students.

Required number of ways =\[{}^{19} C_2 \times^{10} C_2 = \frac{19}{2} \times \frac{18}{1} \times \frac{10}{2} \times \frac{9}{1} = 7695\]

  Is there an error in this question or solution?
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RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 5.2 | Page 15
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