Find in how many ways can
(i) at least one fruit be selected ?
(ii) one fruit of each type be selected?
(iii) at least one fruit of each type be selected ? from 5 oranges, 7 mangoes and 8 bananas?

Explanation

(i) No. of ways of selecting at least one fruit
`= (5 +1) (7+1) (8+1)-1`
`= 6 xx 8 xx 9 - 1`
`= 432 - 1 = 431`
(ii) No. of ways of selecting one fruit of each type `=.^(5)C_(1) xx .^(7)C_(1) xx.^(8)C_(1) = 5 xx 7 xx 8 = 280`.
(iii) No. of ways of selecting at least one orange `= 2^(5) - 1 = 31`
No. of ways of selecting at least one mango `= 2^(7) - 1 = 127`
No. of ways of selecting at least one banana `= 2^(8) - 1 = 255`
`:.` No. of ways of selecting at least one fruit of each type `= 31 xx 127 xx 255 = 1003935`