How-many-even-numbers-between-3000-and-7000-can-be-formed-using-the-digits-2-3-4-5-6-and-8-if-repetition-of-digits-is-not-allowed-

Question Number 883 by 112358 last updated on 12/Apr/15

H o w m a n y e v e n n u m b e r s

b e t w e e n 3000 a n d 7000 c a n b e

f o r m e d u s i n g t h e d i g i t s

2, 3, 4, 5, 6 a n d 8 i f r e p e t i t i o n

o f d i g i t s i s n o t a l l o w e d ?

Answered by prakash jain last updated on 12/Apr/15

First digits 3, 5 = 2

Last digit (2, 4, 6, 8) = 4

Middle two digits^{4} P_{2} = \frac{4!}{2!} = 12

Total with first digits 3, 5 = 2 \times 4 \times 12 = 96

First digit 4, 6 = 2

Last digits (2, 6, 8) or (4, 6, 8) = 3

Middle two digits^{4} P_{2} = \frac{4!}{2!} = 12

Total with first digits 4, 6 = 2 \times 3 \times 12 = 72

Total = 72 + 96 = 168

Commented by 112358 last updated on 12/Apr/15

T h a n k s!

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