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From Karnataka Open Educational Resources
Activity-permutations and combinations problems (view source)
Revision as of 09:08, 10 July 2014
, 09:08, 10 July 2014→Problem 1
Therefore by counting principle total number of ways that a 3-digit number can be formed using 0,1,2,3 and 4 are 4X4X3=48 numbers
Therefore by counting principle total number of ways that a 3-digit number can be formed using 0,1,2,3 and 4 are 4X4X3=48 numbers
=Problem 2=
'''How many 4-digit numbers can be formed using the digits 1,2,3,7,8 and 9 (repetations not allowed)'''<br>
#How many of these are less than 6000?<br>
#How many of these are even?<br>
#How many of these end with 7?<br>
'''Interpretation'''<br>
#using the digits 1,2,3,7,8,9 we have to form 4-digit numbers and also find the numbers that are less than 6000 <br>
#using the digits 1,2,3,7,8,9 how many 4-digit even numbers can be formed.<br>
#using the digits 1,2,3,7,8,9 how many 4-digit numbers can be formed those are ends with 7 or the four digit numbers that are having 7 in unit place.<br>
'''Concepts:'''
#Place value<br>
#when forming a 4-digit number '0' can't occupy the thousands place if it occupies then it becomes 3-digit number<br>
#how to fill the places wheather to start from the unit place or thousands place (in case of the given numbers contain '0')<br>
#if one place is filled with an number then how many digits are left to be filled and how many numbers are there to be left for filling<br>
#should know the charecteristic of the numbers which are less then 6000<br>
#one should remember that only the numbers of 4-digits which are less than 6000 are to be find out not the total numbers which are less than 6000 (total numbers less than 6000 can be 4-digits,can be 3-digits,can be 2-digits and can also be of single digit)<br>
#while forming even numbers one should remember that the number so fomed should end in a even number (0,2,4,6 or 8) or the unit place must be filled with either 0,2,4,6 or by 8 only<br>
#while forming odd numbers one should remember that the number so fomed should end in a odd number (1,3,5,7 or 9) or the unit place must be filled with either 1,3,5,7 or by 9 only<br>
#application of fundamental principle of counting <br>
'''Solution:'''<br>
*'''Thousands Place:''' To form the 4-digit numbers which are less than 6000 the thousands place must be filled with the number which is less than 6 so from the given set of number we can fill it by either 1,2 or by 3 i.e in 3 different ways<br>
*'''Hundreds Place:''' after filling one place we left with 5 numbers so hundreds place can be filled with any of these in 5 different ways<br>
*'''Tens Place:''' with remaing 4-numbers the tens place can be filled in 4 different ways<br>
*'''Unit Place:''' simillarly the unit place can be filled in 3-different ways<br>
Hence by fundamental principle of counting total number of ways =3X5X4X3=180 numbers
*while forming the even number unit place must be filled by either by 2 or 8 from the given set of numbers ( 1,2,3,7,8 and 9)<br>
#unit place-2 ways<br>
#thousands place-5 ways<br>
#Hundreds place -4 ways<br>
#tens place-3 ways <br>
Hence by fundamental principle of counting total number of ways =2X5X4X3=120 numbers
*'''numbers ending in 7'''
#unit place -1way (i.e unit place can be filled by 7 only)<br>
#thousands place-5 ways<br>
#Hundreds place -4 ways<br>
#tens place-3 ways <br>
Hence by fundamental principle of counting total number of ways =1X5X4X3=60 numbers
