Question

ry These
1. Give five examples where the number of things counted would be more than
6-digit number​

Answer 1

Answer:

Step-by-step explanation:

Nature gives us everything it makes us live well

Answer 2

Step-by-step explanation:

$\sf \underline \blue{given}$

• Use the fact that the arrangement of n different things taken all at a time is given by n!.
• generate five examples where the number of things counted would be more than 6-digit numbers.

$\: \sf \underline \blue{\:to \: \: find \: : }$

• Find the value of n when the number of digits in n! exceeds 6 digits.

Complete step-by-step solution -

For the number of digits in n! to be more than 6, we can select the value of n such that the power of 5 in n! is more than 6.

So, if we take n = 30, we have the power of 5 in 30! equals

$\rm\bigg[ \frac{30}{5} \bigg] + \bigg[ \frac{30}{25} \bigg] = 6 + 1 = 7, and \: hence \: 30! \\ \\ \rm \: Will \: have \: more \: then \: six \: digits$

Hence the five different examples where the number of things counted will be more than six-digit number are:

[i] The number of ways in which 30 persons can be

[ii] The number of 30 letter long words that can be formed using all the 30 letters of an alphabet. This is equal to 30! seated in a line. This is equal to 30!

[iii] The number of paths between two vertices in a complete graph of 30 vertices $(k _{30})$This is equal to 30!.

[iv]The number of subsets of a set of cardinality$\tt.30(∵ \: \: {2}^{30} > 999999)$

[v] The number of relations from A to B where n(A) = 5

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Note: Alternatively, we can think of examples from nature where the number of things to be counted is greater than a six-digit number like:

[i] The number of stars in the universe. The estimated number is about 1 billion trillion stars.

[ii] The number of atoms in 1 mole. This is equal to Avagadro's number which is approximately equal to 6.022 x 10²³

[iii] The number of microorganisms in a square metre of soil. There are approximately 10⁹ bacteria, 10⁹ protozoa, etc. in a square metre of soil.

[iv] Number of species of various organisms. The estimated number is about 1 trillion.

[v] Number of cells in the human body. The estimated number is about 37 trillion in a full-grown human body. estimated number is about 1 trillion.