Question

a farmer buys 3 cows ,2 goats and 4 hens from a man who has 4 cows ,3 goats and 8 hens ,how many choices does the farmer have?? ​

Answer 1

Answer:

3 choices

Step-by-step explanation:

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Answer 2

Given Data: Farmer buys 3 cows, 2 goats and 4 hens.

                     The man has 4 cows ,3 goats and 8 hens.

To Find: Choices of the farmer.

Solution:

• Solving this problem by factorial method and arranging in matrix form.
• By multiplying the possibilities we can find the choices of the farmer.

                  $\left[\begin{array}{c}4&3\end{array}\right] \left[\begin{array}{c}3&2\end{array}\right] \left[\begin{array}{c}8&4\end{array}\right]$  $= \frac{4!}{3!(4-3)!}$ × $\frac{3!}{2!(3-2)!}$ ×$= \frac{8!}{4!(8-4)!}$.

• The top row is the man's animals and the bottom is the farmer's animals.
• With the man's options we can find the farmers choice.
• Let the choice is X.

                                     X =    $\frac{1.2.3.4}{1.2.3(1)}$  ×  $\frac{1.2.3.}{1.2.(1)}$  ×  $\frac{1.2.3.4.5.6.7.8}{1.2.3.4(1.2.3.4)}$

• Canceling out the numerator and denominator we get,

                                     X = 4 × 3 × 70

                                     X = 840.

• Hence Farmer have 840 choices.