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Q.

A seven digit number of form $a_{1} a_{2} a_{3} a_{4} a_{5} a_{6} a_{7}$ (all digits are different) is randomly formed, then the probability that this will satisfy the condition $a_{1} > a_{2} > a_{3} > a_{4} < a_{5} < a_{6} < a_{7}$ is

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a

$\frac{9}{1134}$

b

$\frac{7}{1134}$

c

$\frac{5}{648}$

d

$\frac{5}{1134}$

answer is A.

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Detailed Solution

Here n(s) = $9 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4$
$n (E) =^{10} C_{7} \times^{6} C_{3}$
Here will be lowest and take any 3 numbers out of selected 6 numbers and arrange in
1 way
$∴ P = \frac{^{10} C_{7} \times^{6} C_{3}}{9.^{9} P_{6}}$

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