Question

A bag contains $2$ fifty rupee notes, $5$ twenty rupee notes and $2$ ten rupee notes. Five notes are taken at random from the bag. The probability that the total value of these $5$ notes is less than $140$ rupees is

• A. $\frac{16}{21}$
• B. $\frac{5}{21}$
• C. $\frac{58}{63}$
• D. $\frac{53}{63}$

Answer 1

The correct option is A $\frac{16}{21}$

The total value of the amount in all the five notes selected will be greater than or equal to $140,$ if the selection is made in the following ways:
(1) $2$ fifty rupee notes and $3$ twenty rupee notes
(2) $2$ fifty rupee notes, $2$ twenty rupee notes and $1$ ten rupee note
$P=1-\{\frac{{}^2{C}_2{\times }^5{C}_3}{{}^9{C}_5}+\frac{{}^2{C}_2\times {}^5{C}_2\times {}^2{C}_1}{{}^9{C}_5}\}$
$=1-\{\frac{10}{126}+\frac{20}{126}\}=\frac{16}{21}$