TAG | p&c
Another question from O Level Additional Mathematics (A-Math).
lijun(: said…
hey. i just want to clarify something that i’m not very sure of.
is nCr x r! = nPr ??
By definition,
nCr = nPr/r!
Well, I never remember this ‘rule’
For example, find the number of ways to form a 3 letter word from a,b,c,d,e
Student #1:
5C1*4C1*3C1
Student #2:
5P3
Both answers are correct though different approaches are taken, so no need to remember the ‘rule’
:)
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 = 5P3Case 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 = 5P3Total 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
:)
The no. of applicants for a job is 15. (i)Calculate the no. of ways in which 6 applicants can be selceted for the interview.
The six selected applicants on a particular day. (ii)Caluculate the no. of ways in which the order of the six interviews can be arranged.
Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.
Who’s up for this challenge?
******************************
Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.
BBB EE RSo there are 3 groups of people and there are 3! ways of arranging these 3 groups
Within BBB group, there are 3! ways of arrange these 3 B people, similar within EE group, there are 2! ways of arrange these 2E people
so Total = Arrange Big Groups * Arrange within each group = 3! * 3! * 2!
