1,248 views
1 votes
1 votes
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?

2 Answers

4 votes
4 votes
numbers starting with 978 => 987_ _ _ _ _ _ _ => 7!
numbers having 45 in 5th and 6th position => _ _ _ _ 45_ _ _ _ => 8!
numbers ending with 123=7!

numbers starting with 978 and having 45 in 5th and 6th position=98745_ _ _ _ _ =>5!
numbers starting with 978 and ending with 123 => 978 _ _ _ _ 123 =>4!
numbers having 45 in 5th and 6th position and ending with 123 => _ _ _ 45 _ _ 123 =>5!

numbers starting with 978, having 45 in 5th and 6th position and ending with 123 => 98745_ _ 123 =>2!

7!+8!+7!-5!-4!-5!+2!

=50,138
1 votes
1 votes
$($begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions$)$ $or$ $($end with the 3 digits 123 $)$

let the $10$ digits be represented as _ _ _ _ _ _ _ _ _ _

987_ 45_ _ _ _  = $5!$

_ _ _ _ _ _ _ 123 = $7!$

987_45_ 123   = $2!$

$N(A\cup B)$

= $N(A)+N(B)-N(A\cap C)$

= $5! +7! -2!$

=$120 +5040 - 2$

=$5158$
edited by

Related questions

0 votes
0 votes
0 answers
1
sushmita asked Sep 22, 2018
866 views
In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that1.) there are exactly 2 consecutive same letters .2.) atleast 3 consecutive same letters ...
0 votes
0 votes
0 answers
2
srestha asked Oct 4, 2018
624 views
$N$ people toss their hat into a bin, randomly shuffled, returned one hat to each person. What is the probability that $5$th person got his own hat?
0 votes
0 votes
0 answers
3