Each of the digits, 1, 1, 2, 3, 3, 4, 6 is written on a separate card. The seven cards are then laid out in a row to form a 7-digit number.
(a) how many distinct 7-digit numbers are there? [answered - might be related, so posting here]
7! / 2!x2! = 1260
(d) How many of these 7-digit numbers start and end with the same digit?
Do we need to consider distinct objects in this question? I don't get it. I have tried different ways but all failed.
Hello, struck!
You and mathaddict are both correct . . .Each of the digits, 1, 1, 2, 3, 3, 4, 6 is written on a separate card.
The seven cards are then laid out in a row to form a 7-digit number.
(a) How many distinct 7-digit numbers are there?
. . . . . . . Right!
(d) How many of these 7-digit numbers start and end with the same digit?
[1] Numbers that begin and end with 1: .
. . The other five digits (2,3,3,4,6} can be arranged in: ways.
[2] Numbers that begin and end with 3: .
. . The other five digits {1,1,2,4,6} can be arranged in: ways.
Therefore, there are: . numbers that begin and end with the same digit.