The digits of the number 1223678bcan be arranged to give many different 7-digits numbers. Find how many different 7-digits numbers can be made if
i) the digits 1,3,7 (in any order) are next to each other.
ii) These 7-digits numbers are even.
i) the digits 1,3,7 (in any order) are next to each other.
ii) These 7-digits numbers are even.
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i;m taking the "b" after 1223678 as a typo
q(i)
take 137 as a "block" internally permutated in 3! ways
2268 + the "block" can be permutated in 5!/2! ways
total 7-digit #s = 3!*5!/2! = 360 <-------
q(ii)
i'm taking that this is a separate q, ie condition for q(i) doesn't apply
if last digit 2 : 6!
if last digit 6 or 8 : 2*6!/2! = 6!
ans: 2*6! = 1440 <-------
q(i)
take 137 as a "block" internally permutated in 3! ways
2268 + the "block" can be permutated in 5!/2! ways
total 7-digit #s = 3!*5!/2! = 360 <-------
q(ii)
i'm taking that this is a separate q, ie condition for q(i) doesn't apply
if last digit 2 : 6!
if last digit 6 or 8 : 2*6!/2! = 6!
ans: 2*6! = 1440 <-------