Question

8. (6 points) How many six-digit numbers with a possible leading zero, but no repeated numbers are there if the digits 7 and 8 must appear in the number and must be next to each other?

Answer 1

we have to find six digit number with possible led ding zero with no repeatation due there and the digit 7 and 8 must appear in the number and must be next to each other. we find it following. way. To find six digit number we have to use digit o, 1, 2,3,4,5,6,7,8,9

according to given condition The digit 7 & 8 must be next to each other. therefore we consider it as one single digit. so it has five choices, and this digit arranged itself in 2! way. now the remaining_four places. I are filled in 8p 4 way. a Totatal number of six digit. _number with possible leading Zero . with no repeated number are there and the digit 7 and 8 must appear. in the number and must be next to each other are.) - 2X 5 X 814 - = 2 x 5 x 8) (8-4)! WE 10 X 8! 10 X 8 X 7 X 6 XS. #161800 which is required answer