questions on division and distribution of objects into groups set 01

(Q). In how many ways 30 identical chocolates be distributed among 5 students ?
Sol:- 
identical object ━ distinct group

number of ways to distribute = ³⁰ ⁺ ⁴C₄
                                                     = ³⁴C₄     Answer

(Q). In how many ways 30 students can be send to 5 class rooms ?
Sol:-

∴ number of ways = 5³⁰     Answer

(Q). In how many ways 20 different articles can be distributed equally among 4 persons ?
Sol:-

                distinct object ━ distinct group
┃
Group size fixed
┃
Group size are equal

∴ Number of ways of division =  
Number of ways to distribute  =   × 4!
=          Answer

(Q). In how many ways 30 identical chocolates be distributed among 5 students such that a particular student Ankit receive at least 1 chocolate ?
Sol:-            identical chocolate ━ distinct group