FMM4 - Revision history

Admin: Admin moved page 52 Challenge Problems/4/Solution to FMM4

2019-11-16T22:09:44Z

Admin moved page 52 Challenge Problems/4/Solution to FMM4

← Older revision	Revision as of 22:09, 16 November 2019
(No difference)

Admin at 22:09, 16 November 2019

2019-11-16T22:09:39Z

← Older revision		Revision as of 22:09, 16 November 2019
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	=The Zeta Monogram=		{{FMM
			\|title=The Zeta Monogram
	~~==Problem=~~=		\|problem=

	Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, last initial) is in alphabetical order with no letter repeated. (For example, ABZ is a valid monogram, but BBZ and QBZ are not.) How many possible monograms are there?		Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, last initial) is in alphabetical order with no letter repeated. (For example, ABZ is a valid monogram, but BBZ and QBZ are not.) How many possible monograms are there?

			\|solution=
	~~==Solution=~~=

	The Zeta family wants little baby Zeta to have a monogram (first initial, middle initial, last initial) that is alphabetical with no letters repeated. The last letter of the monogram must be Z. If the first letter is A, that leaves 26 - 2 = 24 possible letters, ABZ, ACZ, etc. If the first letter is B, that leaves 23 possible letters, BCZ, BDZ, etc. If we repeat this for all possibilities we will get 24 + 23 + 22 + ...		The Zeta family wants little baby Zeta to have a monogram (first initial, middle initial, last initial) that is alphabetical with no letters repeated. The last letter of the monogram must be Z. If the first letter is A, that leaves 26 - 2 = 24 possible letters, ABZ, ACZ, etc. If the first letter is B, that leaves 23 possible letters, BCZ, BDZ, etc. If we repeat this for all possibilities we will get 24 + 23 + 22 + ...
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	Using the formula n(n+1)/2 we can see that 24 + 23 + ... = 24*25/2 = 300		Using the formula n(n+1)/2 we can see that 24 + 23 + ... = 24*25/2 = 300

			}}

	~~{{ChallengeProblemsFlag~~}}

Admin: Admin moved page 52 Challenge Problems/4/Answer to 52 Challenge Problems/4/Solution

2019-11-16T20:49:42Z

Admin moved page 52 Challenge Problems/4/Answer to 52 Challenge Problems/4/Solution

← Older revision	Revision as of 20:49, 16 November 2019
(No difference)

Admin at 20:47, 16 November 2019

2019-11-16T20:47:55Z

← Older revision		Revision as of 20:47, 16 November 2019
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	=The Zeta Monogram=		=The Zeta Monogram=

			==Problem==

	Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, last initial) is in alphabetical order with no letter repeated. (For example, ABZ is a valid monogram, but BBZ and QBZ are not.) How many possible monograms are there?		Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, last initial) is in alphabetical order with no letter repeated. (For example, ABZ is a valid monogram, but BBZ and QBZ are not.) How many possible monograms are there?


	==~~Answer~~==		==Solution==

	The Zeta family wants little baby Zeta to have a monogram (first initial, middle initial, last initial) that is alphabetical with no letters repeated. The last letter of the monogram must be Z. If the first letter is A, that leaves 26 - 2 = 24 possible letters, ABZ, ACZ, etc. If the first letter is B, that leaves 23 possible letters, BCZ, BDZ, etc. If we repeat this for all possibilities we will get 24 + 23 + 22 + ...		The Zeta family wants little baby Zeta to have a monogram (first initial, middle initial, last initial) that is alphabetical with no letters repeated. The last letter of the monogram must be Z. If the first letter is A, that leaves 26 - 2 = 24 possible letters, ABZ, ACZ, etc. If the first letter is B, that leaves 23 possible letters, BCZ, BDZ, etc. If we repeat this for all possibilities we will get 24 + 23 + 22 + ...

Admin: Created page with "=The Zeta Monogram= Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, l..."

2019-10-08T06:15:05Z

Created page with "=The Zeta Monogram= Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, l..."

New page

=The Zeta Monogram=

Mrs. and Mrs. Zeta are expecting a new (gender-neutral) baby. They wish to name their baby such that the baby's monogram (first initial, middle initial, last initial) is in alphabetical order with no letter repeated. (For example, ABZ is a valid monogram, but BBZ and QBZ are not.) How many possible monograms are there?

==Answer==

The Zeta family wants little baby Zeta to have a monogram (first initial, middle initial, last initial) that is alphabetical with no letters repeated. The last letter of the monogram must be Z. If the first letter is A, that leaves 26 - 2 = 24 possible letters, ABZ, ACZ, etc. If the first letter is B, that leaves 23 possible letters, BCZ, BDZ, etc. If we repeat this for all possibilities we will get 24 + 23 + 22 + ...

Using the formula n(n+1)/2 we can see that 24 + 23 + ... = 24*25/2 = 300

{{ChallengeProblemsFlag}}