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Question
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
Solution
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 360 |
| (c) How many numbers are exactly divisible by 25? | (iii) 40 |
| (d) How many of these are exactly divisible by 4? | (iv) 200 |
Explanation:
(a) Total of 4 digit number formed with 1, 2, 3, 4, 5, 6, 7
= 7P4
= `(7 xx 6 xx 5 xx 4 xx 3!)/(3!)`
= 840
(b) When a number is divisible by 2
= 4 × 5 × 6 × 3
= 360
(c) Total numbers which are divisible by 25 = 40
(d) Total numbers which are divisible by 4 (last two digits is divisible by 4) = 200
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