Call-a-7-digit-telephone-number-d-1-d-2-d-3-d-4-d-5-d-6-d-7-memorable-if-the-prefix-sequence-d-1-d-2-d-3-is-exactly-the-same-as-either-of-the-sequences-d-4-d-5-d-6-or-d-5-d-6-d-7-posibly-both-

Question Number 120204 by bemath last updated on 30/Oct/20

C a l l a 7 - d i g i t t e l e p h o n e n u m b e r d_{1} d_{2} d_{3} - d_{4} d_{5} d_{6} d_{7}

m e m o r a b l e i f t h e p r e f i x s e q u e n c e d_{1} d_{2} d_{3}

i s e x a c t l y t h e s a m e a s e i t h e r o f t h e s e q u e n c e s

d_{4} d_{5} d_{6} o r d_{5} d_{6} d_{7} (p o s i b l y b o t h) .

A s s u m i n g t h a t e a c h d_{i} c a n b e a n y o f t h e t e n

d e c i m a l d i g i t s 0, 1, 2, \dots, 9 . F i n d t h e n u m b e r

o f d i f f e r e n t m e m o r a b l e t e l e p h o n e

n u m b e r s

Commented by mr W last updated on 01/Nov/20

2 \times C_{3}^{10} \times 3! \times 7 = 10080

Commented by bemath last updated on 01/Nov/20

thank you sir

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