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Combinations when repetitions are allowed

Let there be 10 gifts of 3 kinds (A,B,C); of which we have 5A,3B,2C

Let there be 10 gifts of 3 kinds (A,B,C); of which we have 5A,3B,2C. If we are supposed to select 7 gifts out of these, what is the probability that we pick a combination of 4A,2B,1C ?

$$\frac{good} {all} = \frac {E_4(A)E_2(B)E_1(C) }{E_7(A+B+C)} \frac {E_1(A)E_1(B)E_1(C) }{E_3(A+B+C)} $$