Given:
P (n, 4) = 12. P (n, 2)
By using the formula,
P (n, r) =\( \dfrac{ n!}{r!(n – r)!}\)
P (n, 4) = \( \dfrac{ n!}{r!(n – 4)!}\)
P (n, 2) =\( \dfrac{ n!}{r!(n – 2)!}\)
So, from the question,
P (n, 4) = 12. P (n, 2)
Substituting the obtained values in above expression we get,
\(\dfrac{ n!}{(n – 4)!} = 12 × \dfrac{n!}{(n – 2)!}\)
Upon evaluating,
(n – 2) (n – 3) = 12
n2 – 3n – 2n + 6 = 12
n2 – 5n + 6 – 12 = 0
n2 – 5n – 6 = 0
n2 – 6n + n – 6 = 0
n (n – 6) – 1(n – 6) = 0
(n – 6) (n – 1) = 0
n = 6 or 1
For, P (n, r): n ≥ r
n = 6 [for, P (n, 4)]
Answered by Aaryan | 1 year agoHow many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
(i) 4 letters are used at a time
(ii) all letters are used at a time
(iii) all letters are used but first letter is a vowel ?
There are 10 persons named P1, P2, P3 …, P10. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?