Question

A bag contains $12$ two rupees coins, $7$ one rupee coins and $4$ half rupee coins If $3$ coins are selected at random, find the probability that:

• A. The sum of three coins is maximum is $\frac{{}^{12}{C}_3}{{}^{23}{C}_3}$
• B. The sum of three coins is minimum is $\frac{{}^4{C}_3}{{}^{23}{C}_3}$
• C. Each coin is of different value is $\frac{336}{{}^{23}{C}_3}$
• D. Each coin is different value is $\frac{236}{{}^{23}{C}_3}$

Answer 1

Answer: (A)

The sum of three coins is maximum is $\frac{{}^{12}{C}_3}{{}^{23}{C}_3}$

Two rupees Coins $=12$

One rupee Coin $=7$

Half rupee Coins $=4$

$3$ Coins are selected at random.

Total number of Coin $=12+7+4=23$

Random selected coin $=3$

Then selected ways ${=}^{23}{C}_3$

$12$ rupees coin selected are 3 Coins ${=}^{12}{C}_3$

Then,

Probability$=\frac{{{}^{12}C}_3}{{{}^{23}C}_3}$

Hence, this is the answer.