How many 4 letter distinct initial can be formed using the alphabets of English language such that the last of the four words is always a consonant?

Permutation and Combination - Quant/Math - CAT 2016 Question 4 the day: September 04, 2003 The question for the day is from the topic Permutation and Combination. Nội dung chính Show Permutation and Combination - Quant/Math - CAT 2016 XLRI XAT TANCET Practice Question Samples 404 Not Found Sponsored Links Challenger of the Day Maths Quotes Placed User Comments GMAT Club Daily Prep Signing up is free, quick, and confidential. Join 700,000+ members and get the full benefits of GMAT Club Registration gives you: Applicant Stats Books/Downloads Hide Show timer Statistics How many 4 letter distinct initial can be formed using the alphabets of English language such that the last of the four words is always constant? How many sets of 4 initials can be made from the letters of the English alphabet? How many 4 letter words can be made from the English alphabet with vowels at the start and end? How many possible four letter code words can be formed using consonants of the English alphabet if repetition is not allowed? Question: How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant? (1) (26^3)*(21) (2) 26*25*24*21 (3) 25*24*23*21 (4) None of these. Correct Answer - (1) Solution: The last of the four letter words should be a consonant. Therefore, there are 21 options. The first three letters can be either consonants or vowels. So, each of them have 26 options. Note that the question asks you to find out the number of distinct initials and not initials where the letters are distinct. Hence answer = 26*26*26*21 = 263 * 21 XLRI XAT TANCET Practice Question Samples Sorted by Subject Algebra, Arithmetic & Geometric Progressions, Averages and Mean, Clocks and Calendars, Data Sufficiency, English Grammar, Function, Geometry, Coordinate Geometry, Mensuration, Trigonometry, Interest, Inequality, Mixtures & Alligations, Number System and Theory, Percentages, Profit & Loss, Permutation & Combination, Probability, Ratio, Proportion, Set Language and Theory, Speed, Time & Distance, Races, Pipes & Cisterns And Work & Time, Miscellaneous, General Knowledge.

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CEO

Joined: 15 Aug 2003

Posts: 2955

How many four letter distinct initials can be formed using [#permalink]

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How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?

1) (26^3)*(21)
2) 26*25*24*21
3) 25*24*23*21
4) 25^3*21

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Manager

Joined: 21 Aug 2003

Posts: 188

Location: Bangalore

[#permalink]

oops.. i am bad at grammer. what do mean by a 'consonant' ?

CEO

Joined: 15 Aug 2003

Posts: 2955

[#permalink]

Vicky wrote:

oops.. i am bad at grammer. what do mean by a 'consonant' ?

AEIOU are vowels

All other alphabets are consonants.

Intern

Joined: 11 Sep 2003

Posts: 2

Location: India

[#permalink]

3) 25*24*23*21

The last letter can be choosen in 21 ways ( 26 consonants - 5 vowels).

Having choosen the last letter, we can chhose the other three letters among 25 letters in 25*24*23

Hence the total number of ways we canchoose is 25*24*23*21

Correct me , if I am wrong.

Intern

Joined: 16 Jul 2003

Posts: 16

[#permalink]

A.
There are no restrictions about repetition. So total possible words with 3 alphabets = 3^26. multiply this by 21( last letter can only be consonant).

Pls. confirm the answer.

CEO

Joined: 15 Aug 2003

Posts: 2955

[#permalink]

random_choice wrote:

3) 25*24*23*21

The last letter can be choosen in 21 ways ( 26 consonants - 5 vowels).

Having choosen the last letter, we can chhose the other three letters among 25 letters in 25*24*23

Hence the total number of ways we canchoose is 25*24*23*21

Correct me , if I am wrong.

The question asks you to find out the number of distinct initials and not initials where the letters are distinct.

First letter can be arranged in 26 ways
Second letter can be arranged in 26 ways
Third letter can be arrranged in 26 ways

last one...NO vowels...so 26- 5 =21 ways

26^3 * 21 ways

Answer A

thanks all
praetorian

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How many 4 letter distinct initial can be formed using the alphabets of English language such that the last of the four words is always constant?

How many sets of 4 initials can be made from the letters of the English alphabet?

How many 4 letter words can be made from the English alphabet with vowels at the start and end?

How many possible four letter code words can be formed using consonants of the English alphabet if repetition is not allowed?