Answer: B. 3,276,000
Step-by-step explanation:
Given : A student number system for a county requires that the student number be 6 characters.
Number of digits (0,1,2,3,4,5,6,7,8,9)=10
Number of letters in English alphabet = 26
When repetition of things is not allowed then we use Permutations.
Number of permutations of m things taking n at a time =[tex]^mP_n=\dfrac{m!}{(m-n)!}[/tex]
Similarly, Number of permutations of 10 numbers taking 4 at a time :
[tex]^{10}P_4=\dfrac{10!}{(6)!}=\dfrac{10\times9\times8\times7\times6!}{6!}=5040[/tex]
Number of permutations of 26 letters taking 2 at a time :
[tex]^{26}P_2=\dfrac{26!}{(2)!}=\dfrac{26\times25\times24!}{24!}=650[/tex]
Now, the possible number of numbers can be make = [tex]5040\times650=3,276,000[/tex]
Hence, the correct answer is options (b).
