Question

Correct answers only please! If you don't know the answer, then please don't guess or say what you think it is.

Answer 1

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 =$^mP_n=\dfrac{m!}{(m-n)!}$

Similarly, Number of permutations of 10 numbers taking 4 at a time :

$^{10}P_4=\dfrac{10!}{(6)!}=\dfrac{10\times9\times8\times7\times6!}{6!}=5040$

Number of permutations of 26 letters taking 2 at a time :

$^{26}P_2=\dfrac{26!}{(2)!}=\dfrac{26\times25\times24!}{24!}=650$

Now, the possible number of numbers can be make = $5040\times650=3,276,000$

Hence, the correct answer is options (b).