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Mathematics 11 Online
OpenStudy (anonymous):

combinations!

OpenStudy (anonymous):

How many 4-digit positive integers are there, where each digit is positive, and no two adjacent digits are same?

OpenStudy (anonymous):

can you help?? @Nnesha

OpenStudy (ahsome):

Other than Trial and Error, I can't think of anyway @skylark06. Sorry

OpenStudy (anonymous):

it's fine @Ahsome

OpenStudy (haseeb96):

yes @skylark06 what are the numbers?

OpenStudy (anonymous):

like options?? @Haseeb96

OpenStudy (haseeb96):

yes option also but what are those positive integers numbers . because as u know the positive number are infinite

OpenStudy (anonymous):

yeah actually it's combinations problem... no numbers are given. they are asking like what are possibilities. Like how many possibilities is there such that above condition is satisfied.

OpenStudy (anonymous):

well options are A. 1236 B. 3024 C. 4096 D. 4608 E. 6561 @Haseeb96 @ganeshie8

ganeshie8 (ganeshie8):

how many four digit numbers are there in total ?

OpenStudy (haseeb96):

there is mistake in the question or either u dont concentrate on the question i am asking to u what are the positive numbers there given in the question ...

OpenStudy (anonymous):

9000 i guess @ganeshie8

ganeshie8 (ganeshie8):

@Haseeb96 we need to find the total number of positive integers that have no common adjacent digits

ganeshie8 (ganeshie8):

yes so total four digit numbers = 9x10x10x10 = 9000

OpenStudy (anonymous):

yep true )

ganeshie8 (ganeshie8):

lets subtract the numbers that have common adjacent digits from this

OpenStudy (haseeb96):

okay would u tell me how can i do it ? please explain @ganeshie8

ganeshie8 (ganeshie8):

how many ways the common adjacent digits can occur in a four digit number ?

ganeshie8 (ganeshie8):

|dw:1409987277013:dw|

ganeshie8 (ganeshie8):

|dw:1409987303024:dw|

OpenStudy (anonymous):

hmmm yeah like 2 common digits adjacent to each other

ganeshie8 (ganeshie8):

wait a sec, this looks like donkey work there must be a simpler way... lets think a bit

OpenStudy (dan815):

LOL donkey

OpenStudy (anonymous):

lol simple way will be a lot better.. can't we count in hand the possibilities for each digit??

ganeshie8 (ganeshie8):

yeah im thinking the same

ganeshie8 (ganeshie8):

like, number of possibilities for each digit place and multiply them together ?

OpenStudy (anonymous):

yep!! right )

ganeshie8 (ganeshie8):

number of ways of choosing first digit = 9 : |dw:1409987870721:dw| because you cannot choose 0

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