Advertisements
Advertisements
Question
Find n, if nP6 : nP3 = 120 : 1
Solution
nP6 : nP3 = 120 : 1
∴ `("n"!)/(("n" - 6)!) divide ("n"!)/(("n" - 3)!) = 120/1`
∴ `("n"!)/(("n" - 6)!) xx (("n" - 3)!)/("n"!)` = 120
∴ `("n"!)/(("n" - 6)!) xx (("n" - 3)("n" - 4)("n" - 5)("n" - 6)!)/("n"!)` = 120
∴ (n – 3) (n – 4) (n – 5) = 120
∴ (n – 3) (n – 4) (n – 5) = 6 × 5 × 4
Comparing on both sides, we get
n – 3 = 6
∴ n = 9
APPEARS IN
RELATED QUESTIONS
Find n, if nP6 : nP3 = 120: 1.
Find m and n if `""^(("m" + "n"))"P"_2` = 56 and `""^(("m" - "n"))"P"_2` = 12
Show that (n + 1) `""^"n""P"_"r" = ("n" - "r" + 1) ""^(("n" + 1))"P"_"r"`
How many 4 letter words can be formed using letters in the word MADHURI if letters cannot be repeated?
Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object always occurs.
Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object never occurs.
Find the number of permutations of letters of the following word: SHANTARAM
Find the number of permutations of letters of the following word: REPRESENT
Find the number of permutations of letters of the following word: COMBINE
How many distinct 5 digit numbers can be formed using the digits 3, 2, 3, 2, 4, 5
Find the number of distinct numbers formed using the digits 3, 4, 5, 6, 7, 8, 9, so that odd positions are occupied by odd digits.
30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.
Find m and n, if (m+n)P2 = 56 and (m-n)P2 = 12
Find r, if 12Pr–2 : 11Pr–1 = 3 : 14
Show that (n + 1) (nPr) = (n – r + 1) [(n+1)Pr]
A code word is formed by two different English letters followed by two non-zero distinct digits. Find the number of such code words. Also, find the number of such code words that end with an even digit.
Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object always occurs
Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object never occurs
Consider all possible permutations of the letters of the word ENDEANOEL. The number of permutations in which letters A. E. 0 occur only in odd positions, is ______.
Five gifts are to be distributed among seven persons. The number of ways in which this can be done, if there is no restriction on the number of gifts a person can get, is ______.
