how many 10-digit number can be made with odd digits so that no two consecutive digits are the same?

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Solution

Dear student

$t h e o d d d i g i t s a r e 1, 3, 5, 7, 9 n o w t h e f i r s t d i g i t o f t h e n u m b e r c a n b e a n y o f t h e f i v e n u m b e r s 1, 3, 5, 7, 9 s o f i v e w a y s f o r f i r s t d i g i t t h e s e c o n d d i g i t c a n b e t h e n a n y o f t h e r e m a i n i n g f o u r d i g i t s e x c e p t t h e o n e o d d o n f i r s t d i g i t t i s o f o u r w a y s s i m i l a r l y, f o u r w a y s f o r t h e t h i r d d i g i t o f t h e t e n d i g i t n u m b e r S o t o t a l n u m b e r s f o r m e d = 5 \times 4^{9}$

Regards

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