(Q). Let there are 8 oranges, 6 mangoes & 3 apples
(i) How many selection of fruits can be made?
(ii) How many selection of fruits can be made such that at least 1 apple is always included?
(iii) How many selection of fruits can be made such that at least one fruit of each type is always included?
Solution:-
(i). oranges can be selected in (8 + 1) = 9 ways
mangoes can be selected in (6 + 1) = 7 ways
apples can be selected in (3 + 1) = 4 ways
So number of ways of selecting fruit is = 9×7×4 = 252
this also included 1 case when none of the fruits is selected.
Hence total number of ways of selecting 1 or more fruits is 252 – 1 = 251 Answer
(ii). oranges can be selected in (8 + 1) = 9 ways
mangoes can be selected in (6 + 1) = 7 ways
apples can be selected in 3 ways since at least 1 apple is always included.
So number of ways of selecting fruit is = 9×7×3 = 189 Answer
∴ Number of ways of selecting fruit is = 8×6×3 = 144 Answer