Can anyone please give me example for this -
Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is to be always included in each arrangement
= r x P(n-1 r-1)
Think of the formula in this way:
You have n total things, say 10. You need to select r out of those, say 4, such that one of those, say a red ball, is always included.
If you have to select and arrange 4 things out of 10, you use 10p4. Now since the red ball must always be included, we need to select only 3 out of 9 things.
We select and atrrange 3 things out of 9 in 9P3 ways i.e. (n-1)P(r-1). Now the problem leftover is where do you put the red ball? There are 4 places to put the red ball. Before the first thing, before the second thing, before the third thing and after the third thing. Hence, you multiply 9P3 by 4. You get
r * (n-1)P(r-1)
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