GATE Overflow Test Series | Mock GATE | Test 6 | Question: 12

Question

A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasing numbers is _______

Answer 1

Here, we cannot start a number with $0$ and also $0$ cannot come as a later digit as each digit must be in increasing order. Now, we have to select $5$ digits from $9$ possible ones. But instead of permutation, we must use combination because once we select $5$ digits, only one out of the $5!$ permutations will be in increasing order. So, our required answer will be ${}^9C_5 = 126.$

So, the correct answer is $126.$