Question

A purse contains four fifty-paise coins three two-rupees coins and three five-rupee coins If three coins are selected at random then what is the probability of getting the minimum amount?

• A. 1/15
• B. 1/10
• C. 1/30
• D. 1/5

Answer 1

Answer: (C)

1/30

The amount will be minimum, if we choose $3$ coins from the $4$ fifty paise coins.

So, probability that the amount will be minimum $=\frac{Choosing3from4fiftypaisecoins}{Choosingany3fromall10coins}=\frac{{4_C}_3}{{{10}_C}_3}=\frac{\frac{4!}{3!(4-3)!}}{\frac{10!}{3!(10-3)!}}$ Since (${n_C}_r=\frac{n!}{r!(n-r)!}$)
$=\frac{\frac{4!}{1!}}{\frac{10!}{7!}}=\frac{4!\times 7!}{10!}=\frac{4\times 3\times 2\times 7!}{10\times 9\times 8\times 7!}=\frac{1}{30}$