Question

Three integers are selected simultaneously from the set of integers {1,2,3,4,5,.......50}. The probability that the selected numbers are consecutive, is equal to

• A. $\frac{9}{\left(25\right)\left(49\right)}$
• B. $\frac{6}{\left(25\right)\left(49\right)}$
• C. $\frac{3}{\left(25\right)\left(49\right)}$
• D. $\frac{1}{25\left(49\right)}$

Answer 1

The correct option is C $\frac{3}{\left(25\right)\left(49\right)}$

The number of ways of drawing three consecutive numbers is $48$ as the sets can be from $[1,2,3][2,3,4].....$upto$[48,49,50]$
Total ways of choosing three numbers out of 50 is ${{}^{50}C}_3.$
Thus probability $=\frac{48}{{}^{50}{C}_3}=\frac{(48\ast 6)}{(50\ast 49\ast 48)}=\frac{3}{(25\ast 49)}$