Latest TCS Aptitude Question SOLUTION: how many four digits numbers are formed such that the digits are in decreasing order

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how many four digits numbers are formed such that the digits are in decreasing order

Asked In TCS krithika (9 years ago)

Solved abhinav Read Solution (16)

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Read Solution (16) :

abhinav  (9 years ago)

START with 3 = 3_ _ _. You can fill in with digits 0,1,2. Hence 3C3 = 1
START with 4 = 4_ _ _. (0,1,2,3). hence 4C3= 4
START with 5, you have (0,1,2,3,4) to fill in the blanks behind 5, hence 5C3 = 10
START with 6, 6C3=20
7... = 7C3 = 35
8...=8C3 = 56
9...= 9C3 = 84
so ans=1+4+10+20+35+56+84=210

Is this solution Helpfull? Yes (42) | No (16)  

venkat suhas  (9 years ago)

There are 10 digits from 0 to 9.
Selecting 4 digits and they can be arranged in descending order only in 1 way
Total number of ways = 10c4 = 210.

Is this solution Helpfull? Yes (30) | No (1)  

gautam gaurav  (9 years ago)

when we make four digits no starting with 9,we get as
9876,9765,9654,9543,9432,9321,9210.
total seven digit we got
lly for the digits stating from 8,7,6,5,4,3.we get 6,5,4,3,2,1.so total no is=7+6+5+4+3+2+1=28

Is this solution Helpfull? Yes (6) | No (9)  

chaganti anil kumar reddy  (9 years ago)

starts with 1=0
starts with 2=0
starts with 3=1 which is 3210
starts with 4=2 which are 4321,4210 same way
starts with 5=3 6=4 7=5 8=6 9=7 total=28
same as gautam gaurav

Is this solution Helpfull? Yes (5) | No (5)  

virendra tiwari  (9 years ago)

start with 987_ u can fill fill total 7 digit(0,1,2,3,4,5,6);;
start with 986- u can fill total 6 digit(0,1,2,3,4,5);;;
start with 985_ ;;;;;;;;;;;;;;;;;5 digit(0,1,2,3,4)simlarlly next then next
start with 976-;;;;;;;;;;;;;;;;;;;;;;;;;;6 digit
start with 975-;;;;;;;;;;;;;;;;;;;;;;;;;;5 digit and so on u got 84 when u fixed 9,,, 9c3=84,,,then next fixed 8 and find 8c3;
slly 9c3+8c3+7c3+6c3+5c3+4c3+3c3=210

Is this solution Helpfull? Yes (5) | No (1)  

logeswaran  (9 years ago)

ans:126
let us consider the digit
1 2 3 4 5 6 7 8 9
four digit numbers are formed so that
9C4= 9 8 7 6/4 3 2 1
=126

Is this solution Helpfull? Yes (3) | No (8)  

avishek sen  (9 years ago)

Decreasing order lowest 3210
Decreasing order highest 9876
Therefore, In 1st digit---->(3 to 9) =7 numbers
In 2nd digit---->(2 to 8) =7 numbers
In 3rd digit---->(1 to 7) =7 numbers
In 4th digit---->(0 to 6) =7 numbers
Therefore,four digits numbers are formed such that the digits are in decreasing order =(7+7+7+7)=28 (ans.)

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virendra tiwari  (9 years ago)

@ venkat ur ans is in proper way

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Mohd Faisal Rehman  (9 years ago)

Decreasing order lowest 3210
Decreasing order highest 9876
Therefore, In 1st digit---->(3 to 9) =7 numbers
In 2nd digit---->(2 to 8) =7 numbers
In 3rd digit---->(1 to 7) =7 numbers
In 4th digit---->(0 to 6) =7 numbers
Therefore,four digits numbers are formed such that the digits are in decreasing order =(7*7*7*7)= 2401(ans)

Is this solution Helpfull? Yes (2) | No (1)  

Tuhin Chakraborty  (9 years ago)

would like to clear the digits of the number should be in decreasing order, i.e. 3210, 4321, 4210, etc.

Now coming back to ques.
the smallest 4 digit number we see which can be formed by arranging the digits in descending order is 3210.
for staring with 3 we have : 3210
for staring with 4 we have : 4321, 4210
for staring with 5 we have : 5432, 5321, 5210
for staring with 6 we have : 6543, 6432, 6321, 6210
similarly we come an conclusion that there are 28 such numbers that can be formed , i.e. 1+2+3+4+5+6+7=28.

Some used combination to calculate the numbers but u all r getting it wrong when the DECREASING ORDER term comes into existence. And if u think m wrong then tell me any 4 numbers of 4 digits starting with 4 whose digits are arranged in decreasing order as few gave ans using combination like 4C3=4.

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Hanuman Prasad  (9 years ago)

START with 3 = 3_ _ _. You can fill in with digits 0,1,2. Hence 3C3 = 1
START with 4 = 4_ _ _. (0,1,2,3). hence 4C3= 4
START with 5, you have (0,1,2,3,4) to fill in the blanks behind 5, hence 5C3 = 10
START with 6, 6C3=20
7... = 7C3 = 35
8...=8C3 = 56
9...= 9C3 = 84
so ans=1+4+10+20+35+56+84=210

Is this solution Helpfull? Yes (1) | No   

kajjam  (9 years ago)

126
the numbers are
123456789
the solution is 9c4 = 9.8.7.6/4.3.2.1=126

Is this solution Helpfull? Yes | No (2)  

Puja Sharma  (9 years ago)

Well I don't exactly know the answer but one thing to be noticed here is that the digits of a number has to be in a decreasing order

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Souradip Nath  (9 years ago)

Start with 987_ , we have 9876,9875,9874...9870 = 7 possible outcomes.
Next we use 986_, we get 6 outcomes.
In this way we compute 98_ _, and we get 28 outcomes in total.
Then we compute 9*** & finally **** in similar fashion.
In the end we add all possible outcomes to get 179.

Is this solution Helpfull? Yes | No (2)  

M.PRIYANKA  (9 years ago)

@ krithika pls give the solution

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keerti sharma  (9 years ago)

i think 28 is the correct answer

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