Question

Hey guys!!!

Please answer my question.

I'll mark you brainlist.

please do fast.....

How many natural numbers not exceeding 4321 can be formed with the digits 1,2,3 and 4,if the digits can repeat?

The answer is 229.I just need the steps.

Answer 1

$\huge{Hey Dude!!!}$


☆☞ Here is ur answer ☜☆

☆☞ The given digits are 1,2,3 and 4 These digits can be repeated while forming the numbers. So, the number of required four digits natural number can be found as :

☆☞ Consider four digit natural numbers whose digit at thousandths place is 1.

☆☞ Here, Hundredths place can be filled in 4 ways ( using the digits 1 or 2 or 3 or 4 )

☆☞ Similarly : tens place can be filled in 4 ways.  (Using the digits 1 or 2 or 3 or 4)

☆☞ Once place can be filled in 4 ways ( using the digits 1 or 2 or 3 or 4 )

☆☞ Number of four digit natural number whose digit at thousandths place is 1 = 4 × 4 × 4 = 64

☆☞ Similarly : Number of four digit natural numbers whose digit at thousandths place is 2 = 4 × 4 × 4 = 64

☆☞ Number of four digit natural numbers whose digit at thousandths place is 3 = 4 × 4 × 4 = 64

☆☞ Now consider number of four digit natural numbers whose digit at thousandths place is 4 :

☆☞ Here, if the digit at hundredths place is 1, then tens place can be filled in 4 ways and ones place can also be filled in 4 ways.

☆☞ If the digit at hundredths place is 2, then tens place can be filled in 4 ways and ones place can also be filled in 4 ways.

☆☞ If the digit at hundredths place is 3 and the digit at tens place is 1, then ones place can be filled in 4 ways.

☆☞ If the digit at hundredths place is 3 and the digit at tens place is 2, then ones place can be filled only in 1 way so that the number formed is not exceeding 4321.

☆☞ Number of four digit natural numbers not exceeding 4321 and digit at thousandths place is 3 = 4 × 4 + 4 × 4 + 4 + 1 = 37

☆☞ Thus, required number of four digit natural numbers not exceeding 4321 is 64 + 64 + 64 + 37 = 229.

ENJOY...

GOOD BYE!!!

Answer 2

No. has to be less than 4321

so, consider no. s less than 4000

 

1st place:3 ways

2nd place:4 ways

3rd palce:4 ways

4th place:4 ways

therefore, 3*4*4*4=192

 

now consider no.s starting with 4

2nd place can be filled in 2 ways (1&2) as no. has to be less than 4321

1st place:1 way

2nd place:2 ways

3rd palce:4 ways

4th place:4 ways

therefore,1*2*4*4=32

 

now consider no.s starting with 4 and followed by 3

case 1: 432_ → 1 way

case 2:431_ → 4 ways

therfore , 1+4= 5 ways

 

So , total no. of numbers formed= 192+32+5=229