Increasing number in Six digit

Let $\ x_1\ x_2\ x_3\ x_4\ x_5\ x_6$ be a six digit number, find the number of such numbers.

Case 1) $\ x_1 <\ x_2 <\ x_3 <\ x_4 <\ x_5<\ x_6$

Case 2) $\ x_1 <\ x_2 <\ x_3$=$\ x_4 <\ x_5<\ x_6$

Case 3) $\ x_1 <\ x_2 <\ x_3$ $\le$ $\ x_4 <\ x_5<\ x_6$

I have no idea how to approach this problem ,

• Least number is 123456 and the greatest is 456789 – Samar Imam Zaidi Oct 20 '17 at 11:01
• Hint: For case $(1)$, try ${9\choose 6}$. Why does that help? – AnotherJohnDoe Oct 20 '17 at 11:07

Consider choosing $6$ distinct digits from $\{1,2,3,4,5,6,7,8,9\}$
• case 1: The 6 chosen digits can be arranged in only one order. Hence the answer is $\binom{9}{6}$
• case 2: we need to choose only $5$ digits as $2$ of $6$ are equal. So the answer is $\binom{9}{5}$