A box contains 12 two rupee coins, 7 one rupee coins and 4 half rupee coins. If 3 coins are selected at random, find the probability that
(i) sum of three coins is maximum
(ii) each coin is of different value
(iii) selection contains atleast one rupee coin
(iv) all selected 3 coins have same value

Answer

(a) `(.^(12)C_(3))/(.^(23)C_(3))`
(b) `(12 xx 7 xx 4)/(.^(23)C_(3))`
(c) `1 - (.^(16)C_(3))/(.^(23)C_(3))`
(d) `(.^(12)C_(3) + .^(7)C_(3) + .^(4)C_(3))/(.^(23)C_(3))`