Four distinct numbers are randomly selected out of set of first 20 natural numbers. Probab

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14.Probability

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Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. Probability that no two of them are consecutive is -

A

$\frac{28}{57}$

B

$\frac{20}{63}$

C

$\frac{19}{93}$

D

$\frac{12}{59}$

Solution

Number of ways to choose four non consecutive numbers

$ = \,{\,^{20 – 4 + 1}}{C_4}$

Total ways $=\,^{20} \mathrm{C}_{4}$

Probability $ = \frac{{{\,^{17}}{C_4}}}{{{\,^{20}}{C_4}}} = \frac{{17.16.15 \cdot 14}}{{20.19.18.17}} = \frac{{28}}{{57}}$

Standard 11

Mathematics

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