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 6-digit numbers that can be formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisible by 6 ?
Consider the following statements for a fixed natural number n:
1. C(n, r) is greatest if n = 2r
2. C(n, r) is greatest if n = 2r - 1 and n = 2r + 1
Which of the statements given above is/are correct ?
Let x be the number of permutations of the word ‘PERMUTATIONS’ and y be the number of permutations of the word ‘COMBINATIONS’. Which one of the following is correct ?
What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?
A polygon has 44 diagonals then the number of its sides is
