If repetition of numbers is not allowed then how many numbers of five digits can be formed by using

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22 Jan 2016 How many number

If repetition of numbers is not allowed then how many numbers of five digits can be formed by using 1, 2, 3, 4, 5, if 4 is necessarily taken at hundred's place and 2 is not allowed at unit's place.

OPtion

1) 72
2) 16
3) 12
4) 120
5) 96
6) 18
7) 60
8) 30
9) 15
10)24

Solution

4 is necessarily taken at hundred's place and 2 is not allowed at unit's place,
hence number of methods = 1*3*3*2*1 = 18
You can also check the answer by making different numbers under given conditions.

Option 6)

Correct Option: 6 Best Solution (19)

sugayathri   8 years AGO

3 no's are placed in 3! ways=6

4 is placed in 1 way
2 is placed in 3 ways
=6*1*3=18

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BONAM SRINIVAS   8 years AGO

first 4 is placed in hundred's place in 1 way,next 2 should not in units place so remaining 3 no. placed in 3 ways,now remaining 3 places,here repetition not allowed
10's place is filled in 3 ways now remaining 2 places is filled in 2 ways and last 1 way
therefore total ways=1*3*3*2*1=18 ways

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Vishwadeep Solpankhi   8 years AGO

out of 5 digits, 4 is fixed for hundredths place. remaining 4 digits which are 1,2,3,5 for remaining 4 places.
So, hundredth place can be filled in only 1 way (4)
Digit 2 is not allowed at units place.
so Units place can be filled in 3 ways (1,3,5 (because repetition is not allowed) )
Tens place can now be filled in 3 ways (digit 4 is used for hundredth place and any one digit except 2 is used for units place, so we are left with 3 digits as 2 have been used)
Now, thousands place can be filled in 2 ways
ten thousands place can be filled in 1 way

Answer = No. of ways = 3x3x1x2x1 = 18

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suryakant singh   8 years AGO

4 is fix then we have only 1,2,3,5
2 is not allowed at unit place then
at unit place we have 3 option ...similarly at 10 place we have 3 option then
at next place 2 and then 1 so,we can form 3*3*2*1 numbers means 18

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Yashi Das   8 years AGO

4 in hundred's place ->1way
2 not to be in unit's place -> 3 ways
remaining 3 places can be filled by -> 3*2*1=6ways
therefore,
1*3*3*2*1=18 ways

Like? Yes (2) | No (1)  

neeraja   8 years AGO

1 as 1st digit ----- 4 nos
2 as 1st digit ----- 6 nos
3 as 1st digit ----- 4 nos
5 as 1st digit ----- 4 nos
total 18 nos

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Abhikant Bhave   8 years AGO

3 at units place 3at
tens place 1 at hundreds place 2 at thousand place 1 at ten thousand place
so 3 × 3× 1×2×1

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Digvijay singh tomar   8 years AGO

Since 4 Is fixed at 100th postion.
therefore possibility of putting 4 At 100th place is 1 .

now 2 Can't be placed at unit position.
therefore possibility for unit's position is 3,
i.e. 1,3,5 Can come at unit's place.
now remaining three numbers are put at remaining positions without repitition.
therefore

3*3*1*2*1=18

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vipin pandey   8 years AGO

as hundred place can be filled in only 1 way and unit place can be filled in 3 ways and remaining by 3×2×1

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S VANI   8 years AGO

hundred's place is replaced with only 4.
then unit's place is not replaced with 2 then possible chances for filling unit's digit is 3(remaining no's).
ten's place filled with remaining digits i.e., 3.
thousand's place filled with 2 digits.
tenthousand's place filled with remaining 1 digit.
finally answer =(1*2*1*3*3)=18.

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Parag Wagh   8 years AGO

For no. 4 = 1 place
for 2 = 3 places
for 3 = 3 places
for 5 = 2 places
for 1 = 1 place
total = 1*3*3*2*1 = 18

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sumit kumar   8 years AGO

we call fill hundred's place with 1 way.....(1)
unit place 2 is not allowed so it can be filled with 3 possible way....(2)
repetition is nort allowed so ten's place can fill with 3 ways...(3)
4th place can filled with 2 position way....(4)
5th place can filled with 1 possible way.....(5)
with equation (1) to (5)
total possible way to form a number is 1*2*1*3*3=18
option 6

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RITESH KUMAR JHA   8 years AGO

keeping 4 at hundred place by 1 way, with ought keeping 2 at unit place. it will 3 way. after that 3 way again by keeping 2 . now by 2 way and last by 1 way again. and at last ans is from unt place to last place= 3×3×1×2×1=18

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Jaydev Dinda   8 years AGO

As per question, 4 has to be at hundred place..
Case 1
if 4 is hundred place and 2 is at unit place then possible arrangements of 5 digit number are 3!*1*1=6
Case 2
If 4 is at hundred place then possible arrangements of 5 digit number are 4!=24.

Hence, 4 at hundred place and 2 is not unit place,
24-6=18
Option 6 (ans)

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v.sudha   8 years AGO

no. of ways of filling 4 in the hundred places=1
remaining 4 numbers in the units place except 2=3
remaining 3 numbers in the tens place =3
2 numbers in thousand place=2
last position=1
total no. of ways=1*2*3*3*1=18 ways

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v.pravalika   8 years AGO

4 in hundred position =1
except 2 remaining 3 digits in units place=3
including 2 tens place=3
thousand place=2
last position=1
total no.=18

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Shyam Sundar   8 years AGO

4 has been decided so we have 4 places to put on .
on unit digit 2 can't come so there is possibility of using 3 no.s 1,3,5 so for 3 ways and for tens we'll have again three including 2 but one no. has been put in unit place .
So for it 3 ways and so for thousand place 2 and ten thousands place 1 .
1*2*3*3

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Rajani Chaganti   8 years AGO

4 is fixed..so it can be arranged in one way
2 should not be arranged in units place.so it can be arranged in 3 ways..
then remaining numbers are arranged in 3! ways..so
1×3×6=18 ways

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Saleel Kulkarni   8 years AGO

possible nos at hundred's place =1
at unit's place = 3 as no 2 is not allowed
at ten's place = 3
at thousand = 2
at ten thousand = 1
1*3*3*2*1=18

Option 6)

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