How-many-four-digit-numbers-between-2000-and-4000-can-be-formed-from-the-numbers-0-1-2-3-4-and-5-if-repitition-is-allowed-

Question Number 125548 by Don08q last updated on 12/Dec/20

How many four - digit numbers

between 2000 and 4000 can be formed

from the numbers 0, 1, 2, 3, 4 and 5

if repitition is allowed ?

Commented by liberty last updated on 13/Dec/20

l e t t h e n u m b e r A B C D w h e r e 2000 < A B C D < 4000

c a s e (1) \underset{2, 3 [}{A} \underset{1, 2, 3, 4, 5]}{B C D} = 2 \times 5 \times 6^{2} = 360

c a s e (2) \underset{2, 3}{A} \underset{0}{B} \underset{[1, 2, 3, 4, 5]}{C} D = 2 \times 1 \times 5 \times 6 = 60

c a s e (3) \underset{2, 3}{A} \underset{0}{B} \underset{0}{C} \underset{[1, 2, 3, 4, 5]}{D} = 2 \times 1 \times 1 \times 5 = 10

c a s e (4) \underset{3}{A} \underset{0}{B} \underset{0}{C} \underset{0}{D} = 1 \times 1 \times 1 \times 1 = 1

t o t a l l y = 431

Commented by bemath last updated on 12/Dec/20

i t h i n k y o u r a n s w e r c o r r e c t s i r

Answered by Olaf last updated on 12/Dec/20

The first digit is 2 or 3 \Rightarrow 2 possibilities .

For the 3 other digits \Rightarrow 6 possibilities .

2 \times 6^{3} = 432

Here we obtain the possibilities

between 2000 and 3555 .

But 4000 is a possibility too .

\Rightarrow 432 + 1 = 433 possibilities .

Commented by malwaan last updated on 12/Dec/20

m r o l a f

I t h i n k t h e r i g h t a n s w e r i s

432 - 2 = 430

t h e q u e s t i o n i s b e t w e e n 2000

a n d 4000

I f t h e q u e s t i o n w a s f r o m 2000

t o 4000 t h e n t h e a n s w e r w i l l

b e 432

Commented by malwaan last updated on 12/Dec/20

s o r r y

I a m n o t s u r e

Commented by mr W last updated on 12/Dec/20

f o r 2000 ⩽ x ⩽ 4000 t h e a n s w e r i s

2 \times 6^{3} + 1 = 433

f o r 2000 < x < 4000 t h e a n s w e r i s

2 \times 6^{3} - 1 = 431

Commented by Don08q last updated on 12/Dec/20

Yes . 431 is the correct answer . ✓ ✓

Commented by Olaf last updated on 13/Dec/20

Sorry, my english is not fluent .

In my language, “ {between}^{″} means ⩽

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