A sleeper coach in a train has 8 lower berths, and 10 upper berths. Find the number of ways of arranging 18 persons in it, if 3 children want to go upper berth and 4 old people cannot go to the upper berth. A sleeper coach in a train has 8 lower berths, and 10 upper berths. Find the number of ways of arranging 18 persons in it, if 3 children want to go upper berth and 4 old people cannot go to the upper berth.
Answers
¹¹C₄ * 10! * 8 ! is the number of ways arranging 18 persons in 8 lower berths, and 10 upper berths when 3 children want to go upper berth & 4 old people cannot go to the upper berth.
Step-by-step explanation:
3 children want to go upper berth
4 Old People can not go to upper berth means will go to Lower berth
Remaining people = 11
out of 11 , 4 need to go lower berth & 7 to upper berth
this Selection can be done by
¹¹C₄ or ¹¹C₇ Ways
8 Lower berths can be arranged in 8! ways
10 upper berths can be arranged in 10! Ways
Total arrangement = ¹¹C₄ * 10! * 8 !
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4.828336e13 is the Answer
Step-by-step explanation:
As per the Given conditions,
I Condition says- 3 Children = Upper Births
II Condition says 4 Old People = Lower Births
III Condition says, Off 11 people,
4 People = Lower Births =
7 People = upper Births =
Further, 10 Upper births can be arranged in 10! ways
& 8 Lower Births can be arranged in 8! ways.
Hence, Total Arrangements =
= (11! x 10! x 8! )/ (11 - 4)!
= 11! x 10! x 8! / 7! x 4!
= (11 x 10 x 9 x 8 ) x (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) x (8 x 7 x 6 x 5)
= 7920 x 3628800 x 1680
= 4.828336e13