Out of 100 students two sections of 40 and 60 are formed If you and your friend are among 100 students what is the probability (i) you both enter the same section (ii)you both enter the different sections

Explanation

Total outcomes i which both the students are in same section from 40 students `=^{98} C_{38}`


Total outcomes in which both the students are in same section out of 60 students `=^{98} C_{58}`


(a) `P` (Both the students enter in in same section)



`=frac{{ }^{98} C_{38}+{ }^{98} C_{58}}{{ }^{100} C_{40}}=frac{frac{98 !}{38 ! 60 !}+frac{98 !}{58 ! 40 !}}{frac{100 !}{40 ! 60 !}}`


`=frac{98 ![frac{1}{3816015 frac{1}{58140} !}.}{frac{100 !}{40 ! 60 !}}`


`=frac{frac{981 times 58 ! times 38 !}{38 ! times 60 ! times 58 ! times 40 !}(40 times 39+60 times 59)}{frac{100}{40 ! 60 !}}`


`=frac{98 !}{40 ! times 60 !} times 5100 times frac{40 ! times 60 !}{100 !}`


...