How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
Number of letters = [all distinct]
Number of vowels = 5 [e, i, o, u, a]
Number of consonants = 3 [q, t, n]
Step I: Tie the vowels together
Step II: Tie the consonants together.
Step III: Mix the bundles and any remaining letter to give 1 + 1 + 0 = 2 letters.
Number of permutations =
Hence, the number of permutations, using, fundamental principle of counting
= 120 x 6 x 2 = 1440
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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed.
Number of digits available = 5
Number of places for the digits = 3.
Number of ways in which place [x] can be filled = 5
m = 5
Number of ways in which place [y] can be filled = 5 [∵ Repetition is allowed]
n = 5
Number of ways in which place [z] can be filled = 5 [∵ Repetition is allowed]
p = 5
∴ By fundamental principle of counting, the number of 3-digit numbers formed. = m x n x p = 5 x 5 x 5 = 125
458 Views
How many 3-digit odd numbers can be formed from the digits 1,2,3,4,5,6 if:
[a] the digits can be repeated [b] the digits cannot be repeated?
[a] Number of digits available = 6
Number of places [[x], [y] and [z]] for them = 3
Repetition is allowed and the 3-digit numbers formed are odd
Number of ways in which box [x] can be filled = 3 [by 1, 3 or 5 as the numbers formed are to be odd]
Number of ways of filling box [y] = 6 [∴ Repetition is allowed]
Number of ways of filling box [z] = 6 [∵ Repetition is allowed]
∴ Total number of 3-digit odd numbers formed
= m x n x p = 3 x 6 x 6 = 108
[b] Number of ways of filling box [x] = 3 [only odd numbers are to be in this box ]
Number of ways of filling box [y] = 5 [∵ Repetition is not allowed]
Number of ways of filling box [z] = 4 [∵ Repetition is not allowed]
∴ Total number of 3-digit odd numbers formed
= m x n x p = 3 x 5 x 4 = 60.
231 Views
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed.
Number of ways in which place [x] can be filled = 5
m = 5
Number of ways in which place [y] can be filled = 4 [∵ Repetition is not allowed]
n = 4
Number of ways in which place [z] can be filled = 3 [∵ Repetition is not allowed]
p = 3
∴ By fundamental principle of counting, the total number of 3 digit numbers formed = m x n x p = 5 x 4 x 3 = 60.
526 Views
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
Event 1: A coin is tossed and the outcomes recorded.
Number of outcomes
Event 2: The coin is tossed again and the outcomes recorded.
Number of outcomes
Event 3: The coin is tossed third time and the outcomes recorded.
Number of outcomes
∴ By fundamental principle of counting, the total number of outcomes recorded =
548 Views
Given 5 flags of different colours, how many different signals can be generated if each signal requires use of 2 flags, one below the other?
Number of ways of finding a flag for place 1 = 5
Number of remaining flags = 4
Number of ways of finding a flag for place 2 to complete the signal = 4
∴ By fundamental principle of counting, the number of signals generated =
991 Views
How many words with or without meaning can be formed using all the letters of the word EQUATION using each letter exactly one?
How many words with or without meaning can be formed using all the letters of the word utopian at a time so that the vowels and consonants occur together?
Therefore, total no. of words `= 2 xx 120 xx 6 = 1440`.