1) In the expansion (x+y+z)^10, write down all terms having x^6 as one of its fa
ID: 3071552 • Letter: 1
Question
1) In the expansion (x+y+z)^10, write down all terms having x^6 as one of its factors.2) Suppose we want to construct strings of digits 0-9 and 26 capital letters A-Z. How many strings of length 10 are there that have a vowel A, E, I, O, U for the first character, a consonant (any letter that is not one of the listed vowels) for the second character, and a digit for the last character 1) In the expansion (x+y+z)^10, write down all terms having x^6 as one of its factors.
2) Suppose we want to construct strings of digits 0-9 and 26 capital letters A-Z. How many strings of length 10 are there that have a vowel A, E, I, O, U for the first character, a consonant (any letter that is not one of the listed vowels) for the second character, and a digit for the last character
2) Suppose we want to construct strings of digits 0-9 and 26 capital letters A-Z. How many strings of length 10 are there that have a vowel A, E, I, O, U for the first character, a consonant (any letter that is not one of the listed vowels) for the second character, and a digit for the last character
Explanation / Answer
First character as vowel can be selected in 5C1 ways
Second letter as consonant can be selected in 21C1 ways
Last character can be selected in 10C1 ways
Apart from that other 7 characters can be any from the available 36 characters, this can be selected in 36^7 ways
Total possible strings of length 10 are 5C1*21C1*10C1*36^7
= 82,282,372,300,800.00
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