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14.Probability
normal
If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is
A
$12/49$
B
$6/49$
C
$9/49$
D
$15/49$
Solution
Total cases $=7 \times 7 \times 7 \times 7=(7)^{4}$
Favourable $ = {\,^7}{{\rm{C}}_2} \times \left[ {{2^4} – 2} \right]$
$\therefore {\rm{P}} = \frac{{{\,^7}{C_2} \times \left( {{2^4} – 2} \right)}}{{{{\left( 7 \right)}^4}}} = \frac{6}{{49}}$
Standard 11
Mathematics
