Question

Counting question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{Their are 4 apples, 5 mangoes and 6 watermelons .}\hspace{.33em}\\~\\
& \normalsize \text{Find the number of ways }\hspace{.33em}\\~\\
& \normalsize \text{i.) I can purchase at least each of them. }\hspace{.33em}\\~\\
& \normalsize \text{ii.) I can purchase at least one of them. }\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

notice that apples have 5 states : {0, 1, 2, 3, 4}
mangoes have 6 states : {0, 1, 2, 3, 4, 5}
watermelons have 7 states : {0, 1, 2, 3, 4, 5, 6}

Answer 3

yes

Answer 4

is this correct
=(2^4-1)*(2^5-1)*(2^6-1)

Answer 5

I believe so

Answer 6

the english is a bit unclear to me
" I can purchase at least each of them"

Answer 7

but it is given 4*5*6 ways

Answer 8

in book

Answer 9

thats the answer for part a) ?

Answer 10

yes

Answer 11

for partb, is the answer 5*6*7 - 1 ?

Answer 12

yes for part b

Answer 13

it seems textbook is treating all the fruit types as indistinguishable @jayzdd

Answer 14

yes , hmm
i guess i treated them as distinguishable

Answer 15

all apples are are identical and so all mango

Answer 16

For the apple choice you can pick
1 apple
2 apples
3 apples
4 apples

a total of 4 ways to select the apples

Then multiply this by the number of selections you can make for mango
1 mango
2 mangoes
3 mangoes
4 mongoes
5 mangoes

a total of 5 choices

and then similarly for the watermelon there are 6 ways to select them

by multiplication principle, 4*5*6

Answer 17

ok

Answer 18

for part b) now include the zero case

Answer 19

For the apple choice you can pick
0 apples, 1 apple, 2 apples, 3 apples , 4 apples

a total of 5 ways to select the apples

Then multiply this by the number of selections you can make for mango
0 mango 1 mango 2 mangoes 3 mangoes 4 mangoes 5 mangoes

a total of 6 ways to select

And then similarly for the watermelon
0 watermelon, 1 watermelon, ... 6 watermelon
there are 7 ways to select them

By multiplication principle, 5*6*7
But the directions say at least one fruit, so we cannot have 0 apple and 0 mangoe, and 0 watermelon. so we subtract 1

Answer 20

like these method in the previuos question there were 5 methods for bulb
so how can i judge distinguishable bulbs or fruits

Answer 21

The bulbs were fixed by the socket, so there was an ordering to them. lightbulb 1, lightbulb2, ... lightbulb 5

Here there is no natural order to the fruits, since they are indistinguishable.
If they want to treat the fruits as distinguishable, the directions would explicitly say it. otherwise assume indistinguishable