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Home / Doubts and Solutions/JEE/Mathematics

Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5,provided that no digit is to be repeated 

Asked by neeraj.unnao 26th December 2016, 10:52 PM
Answered by Expert
Answer:
begin mathsize 16px style We space have space to space find space the space number space of space positive space integers space between space 6000 space and space 7000 space which space are space divisible space by space 5. So comma space we space have space to space fill space up space four space vacant space places space straight _ space straight _ space straight _ space straight _ space by space 10 space different space digits space left parenthesis from space 0 space to space 9 right parenthesis space satisfying space the space given space conditions space and space repetition space of space digits space is space not space allowed. The space thousand apostrophe straight s space place space has space to space be space filled space up space by space the space digit space 6 comma space so space there space is space only space one space way space to space fill space up space this space place. As space the space numbers space are space divisble space by space 5 comma space so space the space unit apostrophe straight s space place space has space to space be space filled space up space either space by space 5 space or space by space 0. Thus comma space there space are space only space 2 space ways space to space fill space up space the space unit apostrophe straight s space place. Now comma space the space hundred apostrophe straight s space place space can space be space filled space up space in space 8 space ways space by space any space of space the space remaining space 8 space digits space because space at space thousand apostrophe straight s space place space and space at space unit apostrophe straight s space place space two space digits space have space already space been space used. Similarly comma space the space ten apostrophe straight s space place space can space be space filled space up space in space 7 space ways rightwards double arrow The space number space of space required space positive space integers space equals space 1 cross times 8 cross times 7 cross times 2 equals 112 end style
Answered by Expert 27th December 2016, 9:33 AM
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