Mathematics: (a)Evaluate each of the following:(i)10! X 20!17! X 9!

(a)Evaluate each of the following:(i)10! X 20!17!

Ответ:

anher

13.02.2022

Mathematics

$10!\:\times \:20!=\:8.82851\:\times\:10^{24}$

$17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}$

Step-by-step explanation:

Given the expression

$10!\times \:20!$

$\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n$

$10!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10$

$20!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20$

Now, multiplying the result

$10!\times \:20!= 1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20$

$10!\:\times \:20!=\:8.82851\:\times\:10^{24}$

Thus, we conclude that:

$10!\:\times \:20!=\:8.82851\:\times\:10^{24}$

Given the expression

$17!\:\times \:9!$

$\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n$

$17!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17$

$9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9$

Now, multiplying the result

$17!\:\times \:9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9$

$17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}$

Thus, we conclude that:

$17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}$

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Ответ:

kevenluna10oytivm

13.06.2020

Mathematics

total bolts=21

total nuts= 12

no of way picking bolt and nut is= 21*12=252

no of way getting thick bolt and thick nuts = 9*7=63

no of way getting medium bolt and medium nut=8*3=24

no of way getting thin bolt and thin nut= 4*2=8

total ways=63+24+8=95

required probability= 95/252=0.3769

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(a)
Evaluate each of the following:
(i)
10! X 20!
17! X 9!

Ответ:

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