The number of combinations that can be formed with 5 oranges, 4 mangoes and 3 bananas when it is essential to take (i) at least one fruit be "k" (ii) One fruit of each kind "m" find 2m−k ?
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Solution
Here, 5 oranges are alike of one kind, 4 mangoes are alike of second kind and 3 bananas are alike of third kind. (i) the required number of combinations (at least one fruit) =(5+1)(4+1)(3+1)20−1=120−1=119=k (ii) The required number of combinations (one fruit of each kind) =5C1×4C1×3C1=5×4×3=60=m