In how many ways can the word MATHEMATICIAN be ... - JAMB Mathematics 2024 Question

Step-by-Step Solution:

Count the total number of letters:

The word "MATHEMATICIAN" has 13 letters.

Identify the frequency of each letter:

• M: 2
• A: 3
• T: 2
• H: 1
• E: 1
• I: 2
• C: 1
• N: 1

Use the formula for permutations of a multiset:

Total permutations = \(\frac{13!}{2! \cdot 3! \cdot 2! \cdot 1! \cdot 1! \cdot 2! \cdot 1!}\) 

Plug in the values:

Total permutations = \(\frac{13!}{2! \cdot 3! \cdot 2! \cdot 1! \cdot 1! \cdot 2! \cdot 1!}\) 

Total permutations = \(\frac{6227020800}{48} = 129729600\) 

The number of ways to arrange the letters in the word MATHEMATICIAN is 129729600.