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$17$ खिलाड़ियों में से, जिनमें केवल $5$ खिलाड़ी गेंदबाज़ी कर सकते हैं, एक क्रिकेट टीम के $11$ खिलाड़ियों का चयन कितने प्रकार से किया जा सकता है, यदि प्रत्येक टीम में तथ्यत: $4$ गेंदबाज़ हैं ?
$3960$
$3960$
$3960$
$3960$
Solution
Out of $17$ players, $5$ players are bowlers.
A cricket team of $11$ players is to be selected in such a way that there are exactly $4$ bowlers.
$4$ bowlers can be selected in $^{5} C_{4}$ ways and the remaining $7$ players can be selected out of the $12$ players in $^{12} C_{7}$ ways.
Thus, by multiplication principle, required number of ways of selecting cricket team
$=\,^{5} C_{4} \times \,^{12} C_{7}=\frac{5 !}{4 ! 1 !} \times \frac{12 !}{7 ! 5 !}=5 \times \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}=3960$