Respuesta :
Answer with explanation:
Number of Distinct Letters in English Alphabet = 26 Capital +26 Small
=52 Alphabets
Total Number of Distinct digits in number system = {0,1,2,3,4,5,6,7,8,9}=10
Account Number of Customers for a certain Company =3 Letters +2 Numbers
Out of 52 Alphabets , 3 Letters can be Chosen in
[tex]=_{3}^{52}\textrm{P}[/tex] ways, since Order of arranging of three alphabets is Important.
Similarly, out of 10 Digits , 2 numbers can be chosen in
[tex]=_{2}^{10}\textrm{P}[/tex] ways, since Order of arranging of three alphabets is Important.
Total Number of Possible Account number
[tex]=_{3}^{52}\textrm{P} \times _{2}^{10}\textrm{P}\\\\=\frac{52!}{(52-3)!}\times \frac{10!}{(10-2)!}\\\\=\frac{52!}{(49)!}\times \frac{10!}{(8)!}\\\\=52\times 51 \times 50 \times 9 \times 10\\\\=11934000[/tex]
