Respuesta :
[tex]\bf \stackrel{permutations}{_nP_r}=\cfrac{n!}{(n-r)!}\qquad\qquad \qquad \stackrel{balloon}{_7P_1}=\cfrac{7!}{(7-1)!}[/tex]
Answer:
The number is:
1260
Step-by-step explanation:
We know that the number of ways of arranging n items is calculated by the method of permutation.
If n letters are to be arranged such that there are [tex]r_1,r_2[/tex] items each of the same type.
Then, the number of ways of arranging is:
[tex]\dfrac{n!}{r_1!\times r_2!}[/tex]
We are asked to find the number of ways of arranging the letters of "Balloon"
There are a total of 7 words such that 'l' occurs two times and 'o' occurs two times.
Hence, the number of ways of arranging them are:
[tex]=\dfrac{7!}{2!\times 2!}\\\\=\dfrac{7\times 6\times 5\times 4\times 3\times 2!}{2!\times 2}\\\\=1260\ ways[/tex]
