2a How many 4digit positive integers have odd third digit AN

2a. How many 4-digit positive integers have odd third digit? ANS. Show steps 2b. How many 6-digit positive integers have first digit greater than last digit? ANS. Show steps: 3a. Lers callthe kind of path that Grimaldi has on page 9 an \"upright\" path. How many upright paths are there from (1,2) to (8,9)? 3b. How many of the paths in problem 3a pass through the point (4,7)? ANS: Show steps: 3e. How many of the paths in problem 3a pass through both of the points (3,5) and (6,7)? 4a. Here\'s a binary word of length 12: As go from the first o down to the last 1, you can count a total of and 61\' and as you count, the number of o\'s is never less than the number of 1\'s. 60s many binary words of length 12 have that property? Show the \"A number of the Catalan sequence in oEIS:

Solution

2a)4 digit positive integer have odd third digit

first digit has 9 possibilities except 0

second digit has 10 possibilities

given third digit is odd so 5 possibilities i.e 1,3,5,7,9

last digit has 10 possibilities

so number of such 4 digit integers = 9*10*5*10=4500