The number of arrangements of the word KANGAR | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The word $KANGAROO$ contains $8$ letters: $K, A, N, G, A, R, O, O$. The letter $A$ appears $2$ times and $O$ appears $2$ times.Total number of arr

Vedclass · Accepted Answer

$7560$

Vedclass · Answer

(D) The word $KANGAROO$ contains $8$ letters: $K, A, N, G, A, R, O, O$. The letter $A$ appears $2$ times and $O$ appears $2$ times.Total number of arrangements $= \frac{8!}{2!2!} = \frac{40320}{4} = 10080$.To find the number of arrangements where $A$'s do not appear together,we subtract the arrangements where $A$'s are together from the total.Treating the two $A$'s as a single unit $(AA)$,we have $7$ units: $(AA), K, N, G, R, O, O$.The number of arrangements where $A$'s are together $= \frac{7!}{2!} = \frac{5040}{2} = 2520$.Therefore,the number of required arrangements $= 10080 - 2520 = 7560$.

The number of arrangements of the word $KANGAROO$ in which $A$'s do not appear together is

Similar Questions

There are $5$ roads from a village to a city. In how many different ways can a villager go to the city and return back?

There are $9$ chairs in a room,and $6$ people are to be seated. One of these chairs is a special chair reserved for a special guest. In how many ways can these people be seated?

If $0 < r < s < n$ and ${}^n P_r = {}^n P_s$,then find the value of $r + s$.

How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

In how many ways can one send $6$ new-year greeting cards to $4$ people?

Vedclass Test Series

Exam Paper Generator

Online Exam Module