Question 1/20: Set 4 - Try Out - General Reasoning (SNBT)

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Faza wants to create a password with a combination of letters and numbers consisting of $5$ digits. The arrangement of the digits is as follows:

NUMBER - NUMBER - LETTER - NUMBER - LETTER

The conditions for each digit are:

The number in the first position is a prime number.
The number in the second position is an odd number less than $7$ .
The letter in the third position is a vowel forming the name "Faza".
The number in the fourth position is chosen from the set $\{0, 4, 6\}$ .
The letter in the fifth position is a consonant forming the name "Faza".

The number of possible password arrangements that Faza can form is ...

Explanation

To determine the number of possible password arrangements, we can use the multiplication rule (filling slots). The password consists of $5$ digits with the pattern: Number - Number - Letter - Number - Letter.

Let's analyze the number of possibilities for each position using the following table:

Position Analysis

Position	Condition Description	Satisfying Set	Number of Possibilities
$1$ (Number)	Single-digit prime number	$\{2, 3, 5, 7\}$	$4$
$2$ (Number)	Odd number less than $7$	$\{1, 3, 5\}$	$3$
$3$ (Letter)	Vowel from the name "Faza"	$\{A\}$	$1$
$4$ (Number)	Chosen from set $\{0, 4, 6\}$	$\{0, 4, 6\}$	$3$
$5$ (Letter)	Consonant from the name "Faza"	$\{F, Z\}$	$2$

Total Calculation

Based on the multiplication rule, the total number of password arrangements is the product of the possibilities at each position:

\text{Total} = 4 \times 3 \times 1 \times 3 \times 2

\text{Total} = 72

Thus, the number of password arrangements that can be formed is $72$ .

Command Palette

Number 1

Explanation

Position Analysis

Total Calculation