CUET PG 2021 — Mathematics PYQ

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Question

CUET PG 2021 — Mathematics PYQ

CUET PG | Mathematics | 2021

How many distinguishable permutations of the letters are there in the word BANANA?

Choose the correct answer:

Explanation

1. Identify the total number of letters and frequencies

The word is BANANA.

Total number of letters ( $n$ ) = $6$
Frequency of B = $1$
Frequency of A = $3$
Frequency of N = $2$

2. Apply the Formula

The formula for the number of distinguishable permutations is:

\text{Permutations} = \frac{n!}{n_1! \cdot n_2! \cdot \dots \cdot n_k!}

Substituting our values:

\text{Permutations} = \frac{6!}{1! \cdot 3! \cdot 2!}

3. Calculation

Calculate the factorials:

$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$
$1! = 1$
$3! = 3 \times 2 \times 1 = 6$
$2! = 2 \times 1 = 2$

Now, plug these into the equation:

\text{Permutations} = \frac{720}{1 \times 6 \times 2}

\text{Permutations} = \frac{720}{12}

\text{Permutations} = 60