how many three digit numbers can be made using only the digits {1, 2, 4, 6, 8, 9} repetition is allowed

Mathematics

1 answer:

natali 33 [55]3 years ago

7 0

Answer:

Step-by-step explanation:

Given data:

{1 ,2 ,4, 6, 8, 9}

Formula for combinations is used since the order does not matter and repetition is allowed.

nCr = (n + r -1) /(r! * (n-1)!) where n is the total number of items and r is the items to be picked

6C3 = (6 + 3 - 1)! /(3! * (6 -1)!

6C3 = 8!/(3! *5!) Simplifying the factorials)

6C3 = 40320/(6*120)

6C3 = 40320/720

6C3 = 56

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Find the 7th term of the geometric sequence whose common ratio is 1/3 and whose first term is 5.

wolverine [178]

Answer:

$t_7 =\frac{5}{729}$

Step-by-step explanation:

We are given that:

First term (a) = 5

common ratio (r) = $\frac{1}{3}$

The nth term of a geometric sequence is given as:

$t_n =ar^{n-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{7-1} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \bigg(\frac{1}{3}\bigg) ^{6} \\\therefore t_7 =5\times \frac{1}{729}\\\\\huge\red{\boxed{\therefore t_7 =\frac{5}{729} }}$