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Question Number 170748 by MathsFan last updated on 30/May/22

$$$$ A number of four different digits is to be formed from the digits 1,2,3,4,5,6,7,8,9.Find how many of them are: i)greater than 4000 ii)less than 6000 iii) divisible by 2 iv) divisible by 5\n

Answered by Rasheed.Sindhi last updated on 30/May/22

$$\bullet \left(i\right)greaterthan4000$$ $$abcd$$ $$a=4,5,...,96ways$$ $$b....8ways$$ $$c.....7ways$$ $$d.......6ways$$ $$Totalnumbers:6\cdot 8\cdot 7\cdot 6=2016$$ $$\bullet \left(ii\right)lessthan6000$$ $$5\cdot 8\cdot 7\cdot 6=1680numbers$$ $$\bullet \left(iii\right)divisibleby2$$ $$unitdigitmaybe2,4,6,8$$ $$4\cdot 8\cdot 7\cdot 6=1344numbers$$ $$\bullet \left(iv\right)divisibleby5$$ $$unitdigitmaybefilledby5only$$ $$1\cdot 8\cdot 7\cdot 6=336numbers$$

Commented byMathsFan last updated on 30/May/22

$$thankyouSir$$

Commented byKledmaniac last updated on 30/May/22

$$$$ $$ithink{there}^{\prime }samistakein\left(ii\right)$$ $$itshouldbe5\cdot 8\cdot 7\cdot 6=1680$$

Commented byAri last updated on 30/May/22

$$yesitismistake$$

Commented byRasheed.Sindhi last updated on 30/May/22

$$\mathcal{T}hankyousirs!{you}^{\prime }reright!$$

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