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Find the number of ways in which 16 constables can be assigned

Question

Find the number of ways in which $16$ constables can be assigned to patrol $8$ villages, $2$ for each.

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Liam Discussed

Find the number of ways in which

16

constables can be assigned to patrol

8

villages,

2

for each.

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Let the villages be

v_{1}, v_{2} ..... v_{8}

Since

2

police are assigned in each villages\,

∴

No. of police for

v_{1} = 16

v_{2} = 14

v_{3} = 12

v_{8} = 2

∴

No. of ways=

^{16} C_{2} \times^{14} C_{2} \times^{12} C_{2} \times^{10} C_{2} \times^{8} C_{2} \times^{6} C_{2} ....... .^{2} C_{2}

\frac{16 !}{21 ! \times 9 !} \times \frac{14 !}{2 ! \times 12 !} \times \frac{12 !}{2 ! \times 10 !} \times ......... \frac{4 !}{2 ! \times 2 !} \times \frac{2 !}{2 !}

= \frac{16 !}{( 2 ! ) ^{8}}

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Question Text	Find the number of ways in which $16$ constables can be assigned to patrol $8$ villages, $2$ for each.
Answer Type	Text solution:1
Upvotes	150