Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.
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Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes?
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways.
=> The first two letters can be chosen in 26*26=676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
=> All the three letters can be chosen in 676*26=17576 ways.
=> maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
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How many different words can be formed using the letters of the word AMPLITUDE?
All 9 letters are different so Number of words possible are 9!
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There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?
Rock can be done in (2^5 - 1) = 32 - 1 = 31 ways.
6 Carnatic songs, choosing at least one, can be selected in 2^6 - 1 = 64 - 1 = 63 ways.
3 Indi pop can be selected in 2^3 = 8 ways
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
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How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
6 digits telephone number can be formed by 10 digits (0,1,2...9)
As Given, each number start with 35.
So we have 8 digits remaining and 4 place.
So, 4 places can be formed in 8*7*6*5=1680.
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There are 20 balls which are red,blue,or green.If 7 balls are green and the sum of red balls and green balls is less than 13, at most how may red balls are ?
Green ball =7
G + R < 13
So, red can be 1 or 2 or 3 or 4 or 5
For atmost red ball take red = 5
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In a meeting between 2 countries each country has 12 delegates. All the delegates of one country shake hands with all delegates of other countries. Find the number of handshakes possible?
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