Mathematics, 04.01.2020 05:31 jordaaan101

If a, b, and c are integers between 1 and 10 (inclusive), how many different combinations of a, b, and c exist such that a

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Answer from: lusa0720

$\fontsize{18}{10}{\textup{\textbf{The number of different combinations is 120.}}}$

Step-by-step explanation:

A, B and C are integers between 1 and 10 such that A<B<C.

The value of A can be minimum 1 and maximum 8.

If A = 1, B = 2, then C can be one of 3, 4, 5, 6, 7, 8, 9, 10 (8 options).

If A = 1, B = 3, then C has 7 options (4, 5, 6, 7, 8, 9, 10).

If A = 1, B = 4, then C has 6 options (5, 6, 7, 8, 9, 10).

If A = 1, B = 5, then C has 5 options (6, 7, 8, 10).

If A = 1, B = 6, then C has 4 options (7, 8, 9, 10).

If A = 1, B = 7, then C has 3 options (8, 9, 10).

If A = 1, B = 8, then C has 2 options (9, 10).

If A = 1, B = 9, then C has 1 option (10).

So, if A = 1, then the number of combinations is

$n_1=1+2+3+4+5+6+7+8=\dfrac{8(8+1)}{2}=36.$

Similarly, if A = 2, then the number of combinations is

$n_2=1+2+3+4+5+6+7=\dfrac{7(7+1)}{2}=28.$

If A = 3, then the number of combinations is

$n_3=1+2+3+4+5+6=\dfrac{6(6+1)}{2}=21.$

If A = 4, then the number of combinations is

$n_4=1+2+3+4+5=\dfrac{5(5+1)}{2}=15.$

If A = 5, then the number of combinations is

$n_5=1+2+3+4=\dfrac{4(4+1)}{2}=10.$

If A = 6, then the number of combinations is

$n_6=1+2+3=\dfrac{3(3+1)}{2}=6.$

If A = 7, then the number of combinations is

$n_7=1+2=\dfrac{2(2+1)}{2}=3.$

If A = 3, then the number of combinations is

n_8=1.

Therefore, the total number of combinations is

$n\\\\=n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8\\\\=36+28+21+15+10+6+3+1\\\\=120.$

Thus, the required number of different combinations is 120.

Learn more#

Question : ow many types of zygotic combinations are possible between a cross AaBBCcDd × AAbbCcDD?

Link :

Answer from: Quest

step-by-step explanation:

abc

Answer from: Quest

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6 = 0.00000180

1.80 x 10-4 = 0.000180 (bigger, or "less small", than the former one)

1.8 x 10-2 = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

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