Question

From a collection of $20$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

• A. $284\times 17$
• B. $285\times 17$
• C. $284\times 16$
• D. $285\times 16$

Answer 1

The correct option is A $284\times 17$

$1,2,3,\mathrm{4......20}$

there are $17$ way for four consecutive number$\left\{\right(1,2,3,4),(2,3,4,5),(3,4,5,6),\dots \dots ,(17,18,19,20\left)\right\}$

numbers ways $={{}^{20}C}_4-17=285\times 17-17=284\times 17$