An AMARGASAURUS is an extinct sauropod dinosaur of the early

An AMARGASAURUS is an extinct sauropod dinosaur of the early Cretaceous period from what is now Argentina that grew to 30-33 feet in length (which was small for a sauropod). In how many ways can letters in AMARGASAURUS be arranged? In how many different ways can the letters in AMARGASAURUS be arranged if the first letter must be a U and the last letter must be a G?

Solution

AMARGASAURUS: 4A\'s , 2R\'s , 2U\'s , 2S

No. of arrangements = m!/(n1!n2!n3!n4!)

m is no. letters in word = 12

n1, n2, n3, n4 = no. of repeteitions of repetietive letters

No. of arrangements = 12!/(4!2!2!2!)

b) If 1 st and last letter are fixed , we have 10 letters to be arranged

with 4A\'s , 2R\'s , 2U\'s , 2S

No. of arrangements = 10!/((4!2!2!2!)

= 3628800/ 32

= 113400

	= 479,001,600/192
	= 2,494,800