Question 13/20: Set 5 - Try Out - General Reasoning (SNBT)

:00

Ziva wants to create a $4$ -digit password consisting of numbers and the letters forming her name with the following conditions:

letter	number	number	number

The first number is a factor of $9$ .
The second number is an odd prime number.
The third number is chosen from $\{2, 3, 4\}$ .

The number of password arrangements that can be formed from these rules is ...

Explanation

To determine the number of possible password arrangements, we can break down the problem by analyzing the possibilities for each digit position separately.

Position Analysis

Each position has specific criteria limiting the characters that can be used. Here is the breakdown of possibilities for each position:

Position	Condition	Valid Choices	Possibilities
1st	Letters forming "ZIVA"	Z, I, V, A	$4$
2nd	Factors of $9$	1, 3, 9	$3$
3rd	Odd prime numbers (1 digit)	3, 5, 7	$3$
4th	Members of set $\{2, 3, 4\}$	2, 3, 4	$3$

Total Calculation

Based on the multiplication principle (counting slot rule), the total number of password arrangements is the product of the possibilities in each position.

\text{Total} = 4 \times 3 \times 3 \times 3 = 108

So, there are $108$ possible password arrangements.

Command Palette

Number 13

Explanation

Position Analysis

Total Calculation