Question

if you choose 2 letters at random from the letters in the word GRADUATION what is the probability that both letters selected will be constants grid your answer in fraction form

Answer 1

Graduation has 10 letters -- 5 constants, 5 vowels
The number of ways this words can be scrambled to end up with the first two constants is 5.4.3.2.1.5.4.3.2.1=14400
The number of ways this words can be scrambled in total is 10.9.8.7.6.5.4.3.2.1=3628800
Therefore, probability of first two being constant is\[\frac{ 14400 }{ 3628800 }=\frac{ 1 }{ 252 }\]