Gmeet combinatorics

Probability Level 2

A typical gmeet video conferencing code looks like:

a b c \textcolor{#FFFFFF}{abc} pqr-abcd-xyz

where each block (separated by -) can contain any English alphabet, irrespective of the other code blocks.

If there are n n such possible codes, what is the tenth root of n n ?


The answer is 26.

Shubhrajit Sadhukhan by Shubhrajit Sadhukhan , 16, India

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2 solutions

p can be any of the 26 alphabets, for each value of p there are 26 possibilities for q, again for each value of q there are 26 possibilities for r, and so on.

n = 26.26.26...26 ⏟ 10 times = 2 6 10 n = \underbrace{26.26.26...26}_{10 \text{ times}} = 26^{10}

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Saya Suka
Jan 20, 2021

Number of alphabet used
= 3 in the first block + 4 in the second + 3 in the last
= 10 in total

Possible alphabet = 26

Answer
= (26^10)^(1/10)
= 26

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