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14.Probability
normal
Three numbers are chosen at random from $1$ to $15$ . The probability that no two numbers are consecutive, is
A
$\frac{{11}}{{32}}$
B
$\frac{{44}}{{91}}$
C
$\frac{{33}}{{64}}$
D
$\frac{{22}}{{35}}$
Solution
Required probability
$ = \frac{{{\,^{13}}{C_3}}}{{{\,^{15}}{C_3}}} = \frac{{\frac{{13 \times 12 \times 11 \times 10!}}{{3! \times 10!}}}}{{\frac{{15 \times 14 \times 13 \times 12!}}{{3! \times 12!}}}}$
$=\frac{13 \times 12 \times 11}{15 \times 14 \times 13}=\frac{12 \times 11}{15 \times 14}=\frac{22}{35}$
Standard 11
Mathematics
