Question

From the sequence of the first $20$ natural numbers, four are selected such that they are not as 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 $284\times 17$

Solution-

Total ways of selecting consecutive no.s are $(1,2,3,4),(2,3,4,5),(3,4,5,6),........,(17,18,19,20)=17$ possible ways

Total ways of selecting non consecutive no.s = Total ways of selecting - Total ways of selecting consecutive no.s

${=}^{20}{C}_4-17$

$=19\times 15\times 17-17$

$=17(19\times 15-1)=284\times 17$

A is correct