There are 26 letters in English such as {a,b,c,,Z}, and there are 10 1-digit num

Question

There are 26 letters in English such as {a,b,c,,Z}, and there are 10 1-digit numbers such as {0,1,2,.,9}. Now , Tom up a code of length 7 out of these 26 letters and 10 numbers without repetition, assuming letters and numbers equally treated. For example , he may use"af6u89i" as one of his codes, yet "af6u89i" is distinct to, say, "fa6u8i9", a rearrangement. What is the total number of choices that he can have? Now, what is the probability that a random selected code having two vowels, three constants and two numbers? Hint. Make three subgroup of 5 vowels {a,e,i,o,u}, 21 remaining consonants and 10 numbers.

Explanation / Answer

so in total there are 36 letters and numbers. a) 36C7 = 8347680 out of the 36 letters and numbers, there are 5 vowels, 21 consonants, and 10 numbers b) (5C2)(21C3)(10C2)/(36C7)= 10*1330*45/834760 = 0.0717

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