Hi Please help with the following question Thanks a Permutat

Hi,

Please help with the following question;

Thanks,

a) Permutations: In how many ways can 6 people be seated on a bench if only 4 seats are available?

b) Combinations: Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed, in how many ways can this be done if one particular physicist must be on the committee ?

Solution

1)
The first seat can be filled with any of 6 & the next be filled with the rest any
of 5, then 4 and then 3.

No. ways of arrangements are = 6*5*4*3 = 360

2)
A committee of 2 Maths from 5 Math, 3 Physics from 7 Physics chosen ways are = 5 C 2 * 7 C 3 = (5 * 4 / 2 * 1) ( 7*6*5/3*2*1) = 10*35 = 350