Example:- Distribute 10 distinct object among 3 person in anyway.
Solution:-
Here 1ˢᵗ object can be distributed in 3 ways.
Similarly 2ⁿᵈj object can be distributed in 3 ways.
3ʳᵈ object can be distributed in 3 ways
⋮
⋮
⋮
⋮
10ᵗʰ object can be distributed in 3 ways
Hence total number of ways of distribution
= 3×3×3×…………..10 times
= 3¹⁰ Answer
(Q). Distribute 100 letters in 10 letter boxes anyway.
Solution:-
1ˢᵗ letter can be distributed in 10 ways.
Similarly 2ⁿᵈ letter can be distributed in 10 ways.
3ʳᵈ letter can be distributed in 10 ways
⋮
⋮
⋮
⋮
100ᵗʰ letter can be distributed in 10 ways.
Hence total number of ways = 10×10×10×…………100 times
=10¹⁰⁰ Answer
(Q). A person has 5 servant at his home. He has 4 friends. He has to invite his friends by giving one letter to each. He tells his servants to invite his friends. In how many ways he can invite his friends.
Solution:-
S₁ F₁
S₂ F₂
S₃ F₃
S₄ F₄
S₅
which servant gives letter to friend will be a way.
∴ F₁ can be invited in 5 ways.
similarly F₂ can be invited in 5 ways
F₃ can be invited in 5 ways
F₄ can be invited in 5 ways
Hence total number of ways = 5×5×5×5
= 5⁴ Answer
(Q). Distribute 10 distinct books among 5 students if one particular person gets exactly 3 books.
Solution:-
& Remaining 7 books will be distributed among remaining 4 students in anyway ⇒ number of ways sof doing this = 4⁷
Hence total number of ways = ¹⁰C₃×4⁷ Answer
(Q). Distribute 10 distinct books among 5 students if each one is entitled to get at most 9 books.
Solution:-
Required Answer = Total number of ways to distribute in any way – number of ways to distribute in which all 10 books are given to any single student
= 5¹⁰ – 5 Answer