In how many ways can the letter of the word RAINBOW be arranged so that only 2 vowels always remain

@ Vinay,

Pls check.

In 6! cases, there will be some cases when group of two selected vowels will be placed next to third vowel which is not allowed.
11 years agoHelpfull: Yes(3) No(2)
Thank you Aman

Answer is 2880

number of ways = 4320 - number of ways so that the third vowel is next to two vowels
= 4320 - (3C2 * 2! * 2! * 5!)
= 4320 - 1440
= 2880
11 years agoHelpfull: Yes(3) No(4)
Number of ways the letter of the word RAINBOW can be arranged so that only 2 vowels always remain together = 3*(6!*2 - 5!*4) = 3*960 = 2880
11 years agoHelpfull: Yes(3) No(1)
@ VINAY SIPANI

while calculating number of ways so that the third vowel is next to two vowels
how did you get (3C2 * 2! * 2! * 5!) can you explain me this part...
because i got (3C2 * 2! * 5!)
11 years agoHelpfull: Yes(1) No(0)
2600
AI,R,N,B,O,W = 6!*2
+
AO,R,I,N,B,W = 6!*2
+
IO,R,B,N,A,W = 6!*2
-
AOI,R,N,B,W = 3!*5!
=2600
11 years agoHelpfull: Yes(1) No(1)
I think 4320 ways because...
2 out of 3 vowels can be arranged in 3p2 ways
and the total letters with 2 vowels as an entity are 6 which can be arranged in 6! ways..
so, 6!*3p2=4320.
10 years agoHelpfull: Yes(0) No(0)
Taking Two Vowels As One Entity , We Get 3P2 *6! = 4320 Ways.
Number Of Ways So That The Third Vowel Is Next To Two Vowels :

VV*CCCC - 1 x 4!
*VV*CCC - 2 x 4!
C*VV*CC - 2 x 4!
CC*VV*C - 2 x 4!
CCC*VV* - 2 x 4!
CCCC*VV - 1 x 4!
so it sums up to 240
so required no of ways is 4320-240 = 4080
9 years agoHelpfull: Yes(0) No(0)

In how many ways can the letter of the word RAINBOW be arranged so that only 2 vowels always remain together?