Q96 / 155 · WBJEE 2018 · Mathematics

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

Correct answer
A
$284 \times 17$
B
$285 \times 17$
C
$284 \times 16$
D
$285 \times 16$

Solution

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

Hence, the correct answer is option: 'A'.

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