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  • 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)10C_2x19C_3

There are 10 professors and 20 lecturers, out of whom a committee of 2 professors and 3 lecturers 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) ^{9}C_1\times ^{20}C_3
d) In how many ways a particular: lecturer is excluded iv)^{10}C_2\times ^{20}C_3



 

Answers (1)

Given that the number of professors is 10 and the number of lecturers is 20

a.In how many ways committee can be formed= ^{10}C_2\times ^{20}C_3

b.In how many ways a particular professor is included= ^{9}C_1\times ^{20}C_3

c.In how many ways a particular lecturer is included= ^{10}C_2\times ^{19}C_2  

d.In how many ways a particular lecturer is excluded= ^{10}C_2\times ^{19}C_3

 So a-iv,  b-iii, c-ii,  d-i

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