Latest TCS Aptitude Question SOLUTION: How many 6 digit telephone numbers can be constructed with the digits 0, 1, 2, ..., 9 if each number starts with 35 and no digit appears more than once?

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How many 6 digit telephone numbers can be constructed with the digits 0, 1, 2, ..., 9 if each number starts with 35 and no digit appears more than once?

Asked In TCS Tanmoy Barman (12 years ago)

Solved chaitanya Read Solution (9)

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Read Solution (9) :

chaitanya  (12 years ago)

the first two digits are fixed. so the rest of the 4 digits can be chosen from 8 remaining digits.

so ans is 8P4= 1680

Is this solution Helpfull? Yes (16) | No (2)  

jyotish r  (12 years ago)

35---- is the phone number format.8 ways of filling 1st blank space.7 ways of filling next blank space. then 6,then 5. therefore we can have 8*7*6*5=1680 ways of filling. hence answer is 1680

Is this solution Helpfull? Yes (11) | No (2)  

phani  (12 years ago)

first 2numbers are 3 and 5.
we should select 4 others numbers from remaining 8 numbers.............
so TOTAL TELEPHONE NUMBERS=8P4=1680

Is this solution Helpfull? Yes (2) | No   

raj  (11 years ago)

According to me answer will be- 1680

Lets mark 6 places for 6 digits..
- - - - - -
At first 2 places numbers are fixed 3 & 5 so no. of ways of selecting them is only 1.
Now at 3rd place the no. of ways of selecting 1 digit from availalbe 8 digits is 8C1
As it is given tht Repeatation is not allowed.
So
For 4th place the no. of ways of selecting 1 digit from availalbe 7 digits is 7C1
similarly for 5th and 6th place...
1 1 8c1 7c1 6c1 5c1

So finally, No of digits will be= 1 * 1 * 8c1 * 7c1 * 6c1 * 5c1
= 1*1*8*7*6*5
= 1680

Is this solution Helpfull? Yes (2) | No   

rahul.r.kalwar  (12 years ago)

i think 25 can be arranged in 2 ways ie.2! and remaing 4 position can be seen by 8p4 ways =2!*1680=3360

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

shwetha P.T.  (12 years ago)

rest is 8 digits
so 8p4=1680

Is this solution Helpfull? Yes (1) | No   

sumit piplani  (11 years ago)

we have to make telephone no. having 6 digits _ _ _ _ _ _ these are 6 places
1 1 8 7 6 5
now we have only one option to fill 1st and 2nd position by 3 and 5 resp.so way of filling these positions is one.now out of 10 digits(0 to9)we are left with 8 digits as repetion is not allowed.so we have 8 choices to fill 3rd position and 7 choices for 4th position and so on.....and so 5 choices to fill 6th position.(now see above in first line). now multiply 1*1*8*7*6*5=1680

Is this solution Helpfull? Yes (1) | No   

Vikram Nair  (11 years ago)

Since there are 6 digits
_ _ _ _ _ _

number starts with 35 so
3 5 _ _ _ _
The trick is to start from the last digit:
Now since there is a 0 in the list we cant place a zero at the final position
so the last digit is found by 8c1 i.e. 8
3 5 _ _ _ 8
Since if we eliminate any number in the last position there are still 8 numbers so the second last position is again 8c1 i.e. 8 and then so on so forth is 7c1 and 6c1.
Therefore the result is 8*8*7*6=2688

Is this solution Helpfull? Yes | No (3)  

Sumati singhal  (7 years ago)

fix two places as 3 5 , now four places are left and from 8 digits they can be filled without repeating,hence can be calculated as : 1*1*5*6*7*8=1680.

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