If nPr = 720 and nCr = 120, then the value of r is:
3
Calculation:
\(720 = \;\frac{{n!}}{{\left( {n\; - \;r} \right)!}}\)
\((n-r)! = \frac{n!}{720}\)
\(120 = \frac{{n!}}{{r!\left( {n\; - \;r} \right)!}}\)
Putting the value of (n - r)! we get
\(120 = \frac{n!}{r! \frac{n!}{720}}\)
r! = 720/120 = 6 (= 3 × 2 × 1)
r = 3
Important Questions from Permutations and Combinations
What is the number of ways that $5$ boys and $5$ girls can be seated in a row so that boys and girls sit alternately?
The number of ways of choosing 21 objects out of 42 objects of which 21 are identical and the remaining 21 are distinct, is:
For a social work, 7 men and 6 women gave their nominations. The committee is formed to select 5 people from the nominated persons in such a way that atleast 3 men are there in the final team. Find the number of ways in which the people can be selected.
The largest coefficient of ( x + 1)20 is:
If 2n+1Pn–1: 2n–1Pn = 3 : 5, then what is the value of n?
