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

Answer 1

Answer: (C)

400

Answer 2

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
$=5 \cdot 4 \cdot 5 \cdot 4$
$=400$