Question: In how many ways can the letters of the word \'BANANA\' be arranged?
Options:
60
30
20
10
Correct Answer: 30
Solution:
The number of arrangements of the letters in \'BANANA\' is 6! / (3!) = 20.
In how many ways can the letters of the word 'BANANA' be arranged?
Practice Questions
Q1
In how many ways can the letters of the word 'BANANA' be arranged?
60
30
20
10
Questions & Step-by-Step Solutions
In how many ways can the letters of the word 'BANANA' be arranged?
Correct Answer: 20
Step 1: Count the total number of letters in the word 'BANANA'. There are 6 letters.
Step 2: Identify how many times each letter appears. 'B' appears 1 time, 'A' appears 3 times, and 'N' appears 2 times.
Step 3: Use the formula for arrangements of letters with repetitions: Total arrangements = Total letters! / (Repeated letters1! * Repeated letters2! * ...).
Step 4: Plug in the values: Total arrangements = 6! / (3! * 2!).
Step 5: Calculate 6! (which is 720), 3! (which is 6), and 2! (which is 2).
Step 7: The final answer is 60, which is the number of ways to arrange the letters of 'BANANA'.
Permutations of Multisets – The arrangement of letters in a word where some letters are repeated is calculated using the formula n! / (n1! * n2! * ... * nk!), where n is the total number of letters and n1, n2, ..., nk are the frequencies of the repeated letters.
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