Total 5 Digit Telephone Numbers - Permutations & Combinations Question

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now let's learn another question

completely based on the fundamental

principle of counting and the question

is how many five digit telephone number

do you in mind that that's a refi busy

telephone number can be constructed

using the digits 0 to 9

okay zero to nine digits can be used if

the each number starts with successive M

that is this is also very very important

starts with six and seven and no digits

appears more than once means reputation

is not allowed cool so let's get it

straight to the question question is

saying we have to make five digit

telephonic numbers so I have five places

one two three four five all right and

the options that I can feel you are here

ten digits zero one two three four five

six seven eight nine all right so there

are ten digits with which I'm going to

make five digit telephonic number and

one thing one thing one thing the

question has already given some

restrictions the telephone number each

numbers which starts with 67 alright so

67 6 7 so first should be 6 and seconds

would be 7 so this is fixed all right so

6 and 7 let me cancel now alright so

this is already blocked all right we

cannot walk out here so there are only

now 3 positions left for us to work out

all right so this position can be filled

by any of the rest element we can fill

this with 0 by 1 or by 2 or by 3 or by 4

or by 5 or by 8 or by 9 alright so how

many options we have 1 2 3 4 5 6 7 8 so

by the 8 different numbers we can fill

this one alright and if we feel this

then one will get sorted this for a

while let's say we feel this by zero for

a while this time supposing we filled

with zero so now we have two different

places to be filled with rest of the

numbers we can fill this either by one

or by two or by 3 or by 5 or by 5 or by

8 or by 9 so options are 1 2 3 4 5 6 7

so there are several options to fill

this one and once you will fill this one

more we'll get to shortage let's say we

fill with 9 for a while and now we're

left to fill one position with rest of

element so to fill this last position we

can choose any one of them we can choose

one we can choose two we can choose

three you can choose four we can choose

five you can choose 8 so options are 1 2

3 4 5 6 all right 6 so the total 5

detail for

then we can prepare that it starts with

67 R now this will work as a 1 alright

and it is going to fill with eight ways

this can fill with seven way this can be

filled with six weeks so total will be

now 8 times 7 times 6 336 so we can

prepare 336 5dg telephonic number that

starts with 67 and contains the numbers

from 0 to 9 when repetition is not a lot

when digits once appears is not going to

appear once again