How many 4 digit numbers divisible by 5 can be formed with the digit 0,1,2,3,4,5,6,7
Answers
Answered by
2
Hi there!
Here's the answer:
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
Forming 4 Digits by using 0, 1, 2, 3, 4, 5, 6, 7
Condition : No. formed has to be divisible by 5
This problem has 2 cases:
Case -(1) : With Repletion of Digits
Case -(2): Without repetition of digits
Divisibility Rule of 5 States that a No. can be divisible by 5 if the unit's place of the No. is either 0 or 5.
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
SOLUTION :
¶¶¶ CASE - 1 :
WITH REPETITION OF GIVEN DIGITS
4 digits : [ _ ] [ _ ] [ _ ] [ _ ]
No. of given digits = 7
No. of Possibilities in units place = 2
(viz., 0 or 5)
No. of Possibilities in tens place = 7
No. of Possibilities in hundreds place = 7
No. of possibilities in thousands place = 6
(Exclude 0, because it will be a 3-digit No. if included)
•°• Total No. of 4-digit No. that can be formed using 0, 1, 2, 3, 4, 5, 6, 7 WITH REPETITION = 6 × 7 × 7 × 2 = 588
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
¶¶¶ CASE - 2 :
WITHOUT REPETITION OF GIVEN DIGITS
Here the 2 cases of unit digit have to be considered separately
Case -(a) : Unit Digit = 0
No. of given digits = 7
4 digits : [ _ ] [ _ ] [ _ ] [ 0 ]
No. of remaining digits = 6
No. of Possibilities in thousands place = 6
Remaining Digits = 5
No. of Possibilities in hundreds place = 5
(other than 0 and thousands place digit)
Remaining Digits = 4
No. of Possibilities in hundreds place = 4
(Other than digit at thousands place and hundreds place)
Case -(b) : Unit Digit = 5
No. of given digits = 7
4 digits : [ _ ] [ _ ] [ _ ] [ 5 ]
No. of remaining digits = 6
No. of Possibilities in thousands place = 5
(Exclude 0, because it will be a 3-digit No. if included)
Remaining Digits = 5
No. of Possibilities in hundreds place = 5
(Including 0 and excluding thousands place digit)
Remaining Digits = 4
No. of Possibilities in hundreds place = 4
(Other than digit at thousands place and hundreds place and 5)
•°• Total No. of 4-digit No. that can be formed using 0, 1, 2, 3, 4, 5, 6, 7 WITHOUT REPETITION
= (6×5×4) + (5×5×4)
= 100 + 120
= 220
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
Hope it helps
Here's the answer:
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
Forming 4 Digits by using 0, 1, 2, 3, 4, 5, 6, 7
Condition : No. formed has to be divisible by 5
This problem has 2 cases:
Case -(1) : With Repletion of Digits
Case -(2): Without repetition of digits
Divisibility Rule of 5 States that a No. can be divisible by 5 if the unit's place of the No. is either 0 or 5.
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
SOLUTION :
¶¶¶ CASE - 1 :
WITH REPETITION OF GIVEN DIGITS
4 digits : [ _ ] [ _ ] [ _ ] [ _ ]
No. of given digits = 7
No. of Possibilities in units place = 2
(viz., 0 or 5)
No. of Possibilities in tens place = 7
No. of Possibilities in hundreds place = 7
No. of possibilities in thousands place = 6
(Exclude 0, because it will be a 3-digit No. if included)
•°• Total No. of 4-digit No. that can be formed using 0, 1, 2, 3, 4, 5, 6, 7 WITH REPETITION = 6 × 7 × 7 × 2 = 588
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
¶¶¶ CASE - 2 :
WITHOUT REPETITION OF GIVEN DIGITS
Here the 2 cases of unit digit have to be considered separately
Case -(a) : Unit Digit = 0
No. of given digits = 7
4 digits : [ _ ] [ _ ] [ _ ] [ 0 ]
No. of remaining digits = 6
No. of Possibilities in thousands place = 6
Remaining Digits = 5
No. of Possibilities in hundreds place = 5
(other than 0 and thousands place digit)
Remaining Digits = 4
No. of Possibilities in hundreds place = 4
(Other than digit at thousands place and hundreds place)
Case -(b) : Unit Digit = 5
No. of given digits = 7
4 digits : [ _ ] [ _ ] [ _ ] [ 5 ]
No. of remaining digits = 6
No. of Possibilities in thousands place = 5
(Exclude 0, because it will be a 3-digit No. if included)
Remaining Digits = 5
No. of Possibilities in hundreds place = 5
(Including 0 and excluding thousands place digit)
Remaining Digits = 4
No. of Possibilities in hundreds place = 4
(Other than digit at thousands place and hundreds place and 5)
•°• Total No. of 4-digit No. that can be formed using 0, 1, 2, 3, 4, 5, 6, 7 WITHOUT REPETITION
= (6×5×4) + (5×5×4)
= 100 + 120
= 220
•°•°•°•°•°<><><<><>><><>°•°•°•°•°•
Hope it helps
Similar questions