Math Question and Answers


Question and Answers Forum

All Questions Topic List
Permutation and Combination Questions
Previous in All Question Next in All Question
Previous in Permutation and Combination Next in Permutation and Combination
Question Number 120431 by john santu last updated on 31/Oct/20

Commented by john santu last updated on 31/Oct/20

$o l d u n s w e r e d q u e s t i o n$
Commented by mr W last updated on 31/Oct/20

$q u e s t i o n i s n o t q u i t e c l e a r f o r m e .$ $a c c o r d i n g t o m y u n d e r s t a n d i n g a$ $m e m o r a b l e n u m b e r i s e . g .$ $123 - 1234 o r 123 - 4123 .$ $s o m y a n s w e r i s$ $2 \times C_{3}^{10} \times 3! \times 7 = 10080$
	Answered by john santu last updated on 31/Oct/20

	$L e t A d e n o t e t h e s e t o f t e l e p h o n e n u m b e r s$ $f o r w h i c h d_{1} d_{2} d_{3} i s t h e s a m e a s d_{4} d_{5} d_{6}$ $a n d l e t B t h e s e t o f t e l e p h o n e n u m b e r s$ $f o r w h i c h d_{1} d_{2} d_{3} c o n c i d e s w i t h d_{5} d_{6} d_{7} .$ $A t e l e p h o n e n u m b e r d_{1} d_{2} d_{3} - d_{4} d_{5} d_{6} d_{7}$ $b e l o n g t o A \cap B i f o n l y i f d_{1} = d_{2} = d_{3} = d_{4} = . . . = d_{7} .$ $H e n c e n (A \cap B) = 10 . T h u s b y I n c l u s i o n - E x c l u s i o n P r i n c i p l e$ $n (A \cup B) = n (A) + n (B) - n (A \cap B)$ $= 10^{3} . 1.10 + 10^{3} . 10.1 - 10$ $= 20, 000 - 10 = 19, 990$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum