A-Math More P & C Qn! On forming numbers


Another question from O Level Additional Mathematics (A-Math).

How many even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated?

Conditions
#1: Even
#2: 5-digit number
#3: no digit is to be repeated

Case 1:When the first digit is odd (must be more than or equal to 5)

2C1 * 5P3 * 3C1

Logic & Reasoning:

first digit: either 5 or 7 so 2C1
last digit: either 2,4 or 6 so 3C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Case 2:When the first digit is even

5P3 * 2C1

Logic & Reasoning:

first digit: 6 so no need to choose just put!
last digit: either 2 or 4 so 2C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Total even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated = Case 1 + Case 2 = 480

:)

Related Post

The Visualization Tool Revisit Hi everyone, Recently I was reading through the last few months of blogpost and I came across this post "The Visualization Tool" so I decided to wr...
Trouble with Integration of Ln & Expo I seem to have trouble now with integrating ln and e. Haha, you are having trouble because you are learning sth you don't have to know at O'Level. ...
How to prepare for Maths common test Hi everyone, The Chinese New Year is just over. Certainly hope you have received lots of gifts, plenty of blessings, many ang paos... Well, I am...
A-Math More Trigo Graphs Another question for O Level Additional Mathematics (A-Math). On the same diagram, sketch the graphs of y=sin 3x & y=cos2x, for x between 0...
Drawing of Trigo Graphs Can you give an example of a drawing of tangent graphs? For eg, 3tan2x + 1, what does each stand for and how do i go about drawing? From the drawing,...

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

2 Responses to A-Math More P & C Qn! On forming numbers

Leave a reply