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(A) The total number of ways to select $4$ numbers from $20$ is given by $^{20}C_{4}$.The number of ways to select $4$ consecutive numbers from $20$ i

Vedclass · Accepted Answer

$284 	imes 17$

Vedclass · Answer

(A) The total number of ways to select $4$ numbers from $20$ is given by $^{20}C_{4}$.The number of ways to select $4$ consecutive numbers from $20$ is $17$ (these are $(1,2,3,4), (2,3,4,5), \ldots, (17,18,19,20)$).The number of ways to select $4$ non-consecutive numbers is the total number of selections minus the number of consecutive selections.$	ext{Required selections} = {}^{20}C_{4} - 17$$	ext{Required selections} = \frac{20 	imes 19 	imes 18 	imes 17}{4 	imes 3 	imes 2 	imes 1} - 17$$	ext{Required selections} = 4845 - 17 = 4828$Calculating the options: $284 	imes 17 = 4828$.Thus, the correct option is $A$.

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

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