Question

2

Answer 1

Answer:

The number of anagrams of the word ESTADÍSTICA is 2,494,800

Step-by-step explanation:

 Here we have ESTADÍSTICA which has 11 letters

2 As, 2 Ss, 2Ts, 2 Is 1 E, 1 D, and 1 C which gives 11 factorial possible ways out of which 2! × 2! × 2! × 2! are repetitions

Hence we have;

$\frac{11!}{2! \times 2! \times 2! \times 2!} = 2494800$

Therefore, there are 2,494,800 anagrams of the word ESTADÍSTICA.

Answer 2

Answer:

They are 2,494,800 anagram in the word ESTADISTICA

Step-by-step explanation:

To find how many anagram that can be made from the word "ESTADISTICA" means to find how many possible ways the word can be arranged.

STEP 1: The word "ESTADISTICA" has 11 letter in it therefore it has 11!

STEP 2: They are some letter that occurs twice in the word "ESTADISTICA". Which are letter S, T, A, and I. The letters that occurs twice be represented as the denominator as 2!.

Therefore we have 2! × 2! × 2! × 2!

STEP3 : The number of anagram that can be formed with the word ESTADISTICA is

11! ÷ (2! ×2! × 2! × 2!)

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39916800

(2! ×2! × 2! × 2!) = (2×1) × (2×1) × (2×1) × (2×1) = 16

Therefore;

39916800 ÷ 16 = 2494800

The word ESTADISTICA can form 2494800 anagrams. In other words it can be rearranged in 2494800 ways.