Question

Sally has 6 red​ flags, 4 green​ flags, and 2 white flags. How many 12​-flag signals can she run up a flag​ pole? She can create nothing signals.

Answer 1

Answer:

Hence, the answer is:

                           13860

Step-by-step explanation:

Sally has 6 red​ flags, 4 green​ flags, and 2 white flags.

i.e. there are a total of 12 flags.

Now, we are asked to find the different number of arrangements that may be made with the help of these 12-flags.

We need to use the method of permutation in order to find the different number of arrangements.

The rule is used as follows:

If we need to arrange n items such that there are $n_1$ number of items of one type,$n_2$ items same of other type .

Then the number of ways of arranging them is:

$=\dfrac{n!}{n_1!\cdot n_2!}$

Hence, here the number of ways of forming a flag signal is:

$=\dfrac{12!}{6!\times 4!\times 2!}$

( since 6 flags are of same color i.e. red , 4 flags are of green color and 2 are of white colors )

$=\dfrac{12\times 11\times 10\times 9\times 8\times 7\times 6!}{6!\times 4!\times 2!}\\\\\\=\dfrac{12\times 11\times 10\times 9\times 8\times 7}{4\times 3\times 2\times 2}\\\\=13860$