Respuesta :
Answer:
The total number of ways of assignment is 314,790,828,599,338,321,972,833,000.
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
In this case we need to determine the number of ways in which the drugs are assigned to each mouse.
It is provided that new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes.
Drug A is to be given to 22 mice.
Compute the number of ways to assign drug A to 22 mice as follows:
[tex]{60\choose 22}=\frac{60!}{22!(60-22)!}\\\\=\frac{60!}{22!\times 38!}\\\\=14154280149473100[/tex]
Now the remaining number if mice are: 60 - 22 = 38.
Compute the number of ways to assign drug B to 22 mice as follows:
[tex]{38\choose 22}=\frac{38!}{38!(38-22)!}\\\\=\frac{38!}{22!\times 16!}\\\\=22239974430[/tex]
Now the remaining number if mice are: 38 - 22 = 16.
Compute the number of ways to assign no drug to 16 mice as follows:
[tex]{16\choose 16}=\frac{16!}{16!(16-16)!}\\\\=1[/tex]
The total number of ways of assignment is:
[tex]N = {60\choose 22}\times {38\choose 22}\times {16\choose 16}\\\\=14154280149473100\times 22239974430\times 1\\\\=314,790,828,599,338,321,972,833,000[/tex]
Thus, the total number of ways of assignment is 314,790,828,599,338,321,972,833,000.
