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-

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

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

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

Commented by MathsFan last updated on 30/May/22

$$thankyouSir$$

Commented by Kledmaniac last updated on 30/May/22

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

Commented by Ari last updated on 30/May/22

$$yesitismistake$$

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

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

Terms of Service
Privacy Policy
Contact: info@tinkutara.com