Mr. A randomly picks 3 distinct numbers from the set ${1, 2, 3........., 9}$ and arranges them in descending order to form a three digit number. Mr. B randomly picks 3 distinct numbers from the set ${1, 2, 3........., 8}$ and also arranges them in descending order to form a 3 digit numbers and Probability that Mr. A’s 3 digit number is greater than Mr. B’s 3 digit number is $\frac{a}{b}$ (where a, b are coprime positive integers) then which of the following is/are TRUE?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$2 a - b = 18$

$a + b = 4$

$a + b = 93$

$2 b - a = 5$

answer is B, C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

When A’s three digit number starts with 9, then it is always greater than B’s three digit number
Required probability = $\frac{8 C_{2}}{9 C_{3}} = \frac{1}{3}$
When 9 is not included $= \frac{{(^{8} C_{3})}^{2} -^{8} C_{3}}{2}$
So, R.P $= \frac{1}{3} + \frac{{(^{8} C_{3})}^{2} -^{8} C_{3}}{{2.}^{9} C_{3} .^{8} C_{3}} = \frac{37}{56}$