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

Given, numbers are $1,2,3 \ldots \ldots \ldots 20$
Here, number of ways of selecting four consecutive numbers $=17$
$\therefore$ Required number of selecting $4$ non-consecutive numbers
$={ }^{20} C_{4}-17$
$=\frac{20 \times 19 \times 18 \times 17}{4 \times 3 \times 2 \times 1}-17$
$=285 \times 17-17 $
$=284 \times 17$