How-many-numbers-greater-than-200-can-be-formed-from-the-digits-1-2-3-4-5-if-no-digit-is-to-be-repeated-in-any-particular-number-

Question Number 151615 by pete last updated on 22/Aug/21

How many numbers greater than 200 can

be formed from the digits 1, 2, 3, 4, 5 if no

digit is to be repeated in any particular

number ?

Answered by mr W last updated on 22/Aug/21

P_{3}^{5} - P_{2}^{4} + P_{4}^{5} + P_{5}^{5} = 288

Commented by pete last updated on 22/Aug/21

Thanks sir, but can you please explain

a little ?

Commented by mr W last updated on 22/Aug/21

3 - d i g i t n u m b e r s :

f r o m 5 d i g i t s y o u c a n f o r m P_{3}^{5} 3 - d i g i t

n u m b e r s . b u t t h e n u m b e r s b e g i n n i n g

w i t h 1 m u s t b e e x c l u d e d, b e c a u s e

t h e y a r e s m a l l e r t h a n 200 . w h e n a

n u m b e r b e g i n n t w i t h 1, t o f o r m t h e

n e x t 2 d i g i t s f r o m t h e o t h e r 4 d i g i t s,

t h e r e a r e P_{2}^{4} w a y s . t h e r e f o r e t h e r e

a r e P_{3}^{5} - P_{2}^{4} 3 - d i g i t n u m b e r s l a r g e r

t h a n 200 .

4 - d i g i t n u m b e r s :

t o f o r m a 4 - d i g i t n u m b e r f r o m 5

d i g i t s t h e r e a r e P_{4}^{5} w a y s . a l l t h e s e

n u m b e r s a r e l a r g e r t h a n 200 .

5 - d i g i t n u m b e r s :

t o f o r m a 5 - d i g i t n u m b e r f r o m 5

d i g i t s t h e r e a r e P_{5}^{5} w a y s . a l l t h e s e

n u m b e r s a r e l a r g e r t h a n 200 .

t o t a l l y w e c a n f o r m

P_{3}^{5} - P_{2}^{4} + P_{4}^{5} + P_{5}^{5} r e q u e s t e d n u m b e r s .

Commented by pete last updated on 26/Aug/21

Thank you sir

Facebook Tweet Pin