Question

Fifteen coupons are numbered 1,2,.....15 respectively. Three coupons are selected at random without replacement . The probability that the maximum number on the selected coupon is 9, is

• A. $4/65$
• B. $3/65$
• C. $1/13$
• D. None of these

Answer 1

The correct option is A $4/65$

Total numbers of ways in selecting three coupons from fifteen coupens without replacement = ${}^{15}{C}_3$

$=\frac{15\times 14\times 13}{1\times 2\times 3}$

= 455.

The numbers of ways in selecting three coupons out of which 9 is the maximum number

= numbers of ways in selecting 2 other coupons with number is from 1 to 8.

${=}^8{C}_2=\frac{8\times 7}{1\times 2}$

= 28.

$\therefore$ Probability that the maximum numbers in the selecting coupons is $9=\frac{28}{455}$

$=\frac{4}{65}$