Permutation and combinations

Question

I am confused with Following formulaes of combination..

1. n!/r!

2. n+k-1 C k

3. (P+1)*2^R where (P+R are total things and P are alike).

4. question such as number of ways of choosing 10 balls out of 15 balls in which 5 are red,8 are green,2 are black.

Anybody please provide me some reference to understand these formulaes related to combination.

Answer 1

in your question, 15 balls are divided in colours!

but i need to take 10 balls.and no condition is given on the colors of that 10 balls.

so i can take any color balls,

simply i have to choose 10 balls from 15  balls ,ehich is ¹⁵C₁₀

Comments

identical balls will change the way to select ..

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yes! the word identical will change

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@Uddipto does that mean by default we consider the balls as distinc when not mentionedt?