Looking for help with problem 4? How many 3-High numbers abc are there, where 1

Question

Looking for help with problem 4?

How many 3-High numbers abc are there, where 1 lessthanorequalto a lessthanorequalto 6, 3 lessthanorequalto b lessthanorequalto 7 and 2 lessthanorequalto c lessthanorequalto 8? On the right side of an auditorium every seal is labeled with its row (A, B, ... ., P) following a 2-digit even numbers from 02 to 36. On the left side of the auditorium, the situation is the same except the seat numbers in each row are odd (from 01 through 35). How many seats are there in the auditorium? How many 4-digit even numbers with no repealing digits are there that are less than 600? In one portion of a city, a telephone number begins with 381, 383 or 385, followed by four digits. How many such telephone numbers are possible? How many such telephone numbers have no digits repeated? How many different 12-bit strings begin with 0101, end with 1100 or have 0110 as the four middle bits? A total of 100 people attending a movie were asked if they normally have popcorn, candy or a soft drink when they go to a movie. They answered: 62 have popcorn. 20 have candy, 70 have a soft drink, a have popcorn and randy. 51 have popcorn and a soft drink, 11 have candy and a soil drink and have all 3. How many have none of these?

Explanation / Answer

let the digit be ABCD now for A we have 5 choices = 1,2,3,4,5

lets first take the case when A is odd so no of choices forA=3, D=5,B=8,C=7

total nos = 3*5*8*7 = 840

lets take the case when A is even so no of choices forA=2, D=4,B=8,C=7

total nos = 2*4*8*7 = 448

total = 1288

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