Question

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?

• A. 380
• B. 360
• C. 400
• D. 520
• E. 480

Answer 1

Answer: (C)

We know that, the odd numbers are
$\{1,3,5,7,9\}$
$\therefore n(a)=5$
Divisible by $3$ are $\{0,3,6,9\},n(b)=4$
Even numbers are $\{0,2,4,6,8\},n(c)=5$
and prime numbers are $\{2,3,5,7\},n(d)=4$
$\therefore$ Four-digit numbers $abcd$ exist
$=5\cdot 4\cdot 5\cdot 4$
$=400$