Q.Using the fundamental principle of counting, find how many 4-digit numbers (with no digit repeated) can be formed using the digits $1,2,3,4,5,6$.

Each of the 4 digit-positions is filled one after another, and because no digit may repeat, the number of choices available shrinks by one at each successive position.

By the Fundamental Principle of Counting, fill the 4 positions of the number one at a time:

• 1st digit: any of the 6 digits, so $6$ choices.
• 2nd digit: any of the remaining 5 digits (no repetition), so $5$ choices.
• 3rd digit: any of the remaining 4 digits, so $4$ choices.
• 4th digit: any of the remaining 3 digits, so $3$ choices.

Total number of 4-digit numbers $= 6\times5\times4\times3 = 360$. …

Multiplying $6\times6\times6\times6=1296$ by mistakenly allowing repetition when the question explicitly says digits may not repeat; also forgetting that the number of choices d …