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The number of five digit numbers divisible by 5 that can be formed using the numbers $0,1,2,3,4,5$ without repetition is
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The correct answer is:
216
The five digit number is formed only when unit place is either 0 or 5 .
Case I. When 0 is in unit place, then rest of numbers can be selected in ${ }^5 P_4$ ways.
$=5 !=120$
Case II. When 5 is in unit place, then rest of numbers can be selected in ${ }^5 \mathrm{P}_4$ ways.
$=5 !=120$
And we have to subtract those cases in which 0 is in thousand place.
The number of ways $={ }^4 P_3=24$
$\therefore$ Required number of ways $=120+120-24$ $=216$
Case I. When 0 is in unit place, then rest of numbers can be selected in ${ }^5 P_4$ ways.
$=5 !=120$
Case II. When 5 is in unit place, then rest of numbers can be selected in ${ }^5 \mathrm{P}_4$ ways.
$=5 !=120$
And we have to subtract those cases in which 0 is in thousand place.
The number of ways $={ }^4 P_3=24$
$\therefore$ Required number of ways $=120+120-24$ $=216$
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