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How many 5-digit numbers can be formed from the digits [#permalink]
11 Nov 2007, 03:53

2

This post was BOOKMARKED

How many 5-digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once in a number ? How many even numbers can be formed ?

In how many ways can 4 consonants and 3 vowels be arranged in a row (a) so that the 3 vowels are always together, (b) so that the first and the last places are occupied by consonants.

Re: more perm to solve [#permalink]
14 Nov 2007, 23:46

Ravshonbek wrote:

In how many ways can 4 consonants and 3 vowels be arranged in a row (a) so that the 3 vowels are always together, (b) so that the first and the last places are occupied by consonants.

(a) consider 3 vowels as one package, 4 consonants as 4 packages. Arranging these 5 packages, we have 5! ways. Besides, 3 vowels arrange within one package in 3! ways. So in total, we have 3!*5! ways to arrange as requested.

(b) there're C(4,1) alternatives for first place; then, there're C(3,1) alternatives for last place. We're left with 2 consonants and 3 vowels to place in between. There're 5! ways to arrange these 5 entities => The number of way for us to arrange as requested is C(4,1)*C(3,1) * 5!

Re: more perm to solve [#permalink]
15 Nov 2007, 06:40

laxieqv wrote:

Ravshonbek wrote:

In how many ways can 4 consonants and 3 vowels be arranged in a row (a) so that the 3 vowels are always together, (b) so that the first and the last places are occupied by consonants.

(a) consider 3 vowels as one package, 4 consonants as 4 packages. Arranging these 5 packages, we have 5! ways. Besides, 3 vowels arrange within one package in 3! ways. So in total, we have 3!*5! ways to arrange as requested.

(b) there're C(4,1) alternatives for first place; then, there're C(3,1) alternatives for last place. We're left with 2 consonants and 3 vowels to place in between. There're 5! ways to arrange these 5 entities => The number of way for us to arrange as requested is C(4,1)*C(3,1) * 5!

Very nice. Thanks.

gmatclubot

Re: more perm to solve
[#permalink]
15 Nov 2007, 06:40

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