There are 10 engineering colleges and five students A, B, C, D, E… - Vidyadip

MCQ

There are $10$ engineering colleges and five students $A, B, C, D, E$ . Each of these students got offer from all of these $10$ engineering colleges. They randomly choose college independently of each other. Tne probability that all get admission in different colleges can be expressed as $\frac {a}{b}$ where $a$ and $b$ are co-prime numbers then the value of $a + b$ is

✓
$814$
B
$731$
C
$1013$
D
$502$

✓

Answer

Correct option: A.

$814$

a
Total no. of cases $=10^{5}$

All students want different colleges so no. of

cases $ = {\,^{10}}{{\rm{C}}_5} \times 5!$

Probability $ = \,\frac{{^{10}{{\rm{C}}_5} \times 5!}}{{{{10}^5}}} = \frac{{189}}{{625}} = \frac{{\rm{a}}}{{\rm{b}}}$

$a+b=189+625=814$

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