How many 4digit positive integers have odd third digit ANS S

How many 4-digit positive integers have odd third digit? ANS.:________________________ Show steps: How many 6-digit positive integers have first digit greater than last digit? ANS.:_______________________ Show steps: Let\'s call the kind of path that Grimaldi has on page 9 an \"upright\" path. How many upright paths are there from (1, 2) to (8, 9)? ANS.:___________________ How many of the paths in problem 3a pass through the point (4, 7)? ANS.:_____________________ Show steps: How many of the paths in problem 3a pass through both of the points (3, 5) and (6, 7)? ANS.:____________________

Solution

2a) to find haw many 4 digit positive number have add thired digit

let ABCD is 4 digit number

since A have 9 choices

now 3rd number is odd therfore

B have 10 choices

C have 5 choices

D have 10 choices

therfore 4 digit positive numbers= 9x5x10x10=4500

2b)

consider 6 digit number ABCDEF

since first digit is greter than last digit

we have Choice of A is 9

and choice for last digit F is 8 (since A>F)

choice for each B ,C,D,E, are 10

therefore 6 digit positive number have first digit greter than last = 9x10x10x10x10x8

=72x10⁴