Question

The number of three digit numbers of the form $xyz$ where $x>y>z$ is

• A. $120$
• B. $720$
• C. $600$
• D. $100$

Answer 1

The correct option is A $120$

Any number contains digits from $0$ to $9$.

To find three digit numbers of the form $xyz$ where $x>y>z$, we just need to find the number of digits formed by selecting digits from $0$ to $9$.

There will be no repetition of digits and $abc$ will be same as $acb$ and $cab$.

So, any selection of three digits from the ten digits $0,1,2,.........,9$ will give the number of the given form.

Since, arrangement of numbers is not possible.So, permutation is not possible here.

Therefore it forms a combination of $10$ numbers.

Thus, the choosing $3$ digits out of $10$ digits is given by ${}^{10}{C}_3=\frac{10!}{7!3!}=\frac{10\times 9\times 8}{3\times 2}=120$

Hence, option A is correct.