Question

please help and please don't scam. itne bhi easy nhi h mere Question. jaldi nhi h. shanti se ek ka to answer de do.​

Answer 1

I think the answer is 1.15

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

↝ There are 3 deck of cards, each deck has 6 cards marked 2, 3, 4, 5, 6, 7.

↝ Since, 1 card is drawn from each deck.

Let assume that

$\rm :\longmapsto\:x_1 \: is \: drawn \: from \: deck \: 1$

$\bf\implies \:2 \leqslant x_1 \leqslant 7$

$\rm :\longmapsto\:x_2 \: is \: drawn \: from \: deck \: 1$

$\bf\implies \:2 \leqslant x_2 \leqslant 7$

and

$\rm :\longmapsto\:x_3 \: is \: drawn \: from \: deck \: 1$

$\bf\implies \:2 \leqslant x_3 \leqslant 7$

According to statement,

$\rm :\longmapsto\:x_1 + x_2 + x_3 = 8$

We know that

Number of ways in which n identical things can be distributed in to r different groups is given by

$\boxed{ \tt{ \: Number \: of \: ways \: = \: ^{n+r-1}C_{r-1} \: }}$

So,

Total number of ways in which one card is drawn from each deck so that sum of 3 cards is 8 is

$\rm \:  =  \:\: ^{8+3-1}C_{3-1} \:$

$\rm \:  =  \:\: ^{10}C_{2} \:$

$\rm \:  =  \:\dfrac{10 \times 9}{2 \times 1}$

$\rm \:  =  \:45$

Hence,

$\red{\rm \implies\:\boxed{ \tt{ \:Number \: of \: ways \: = \: 45 \: }}}$

Additional Information :-

$\boxed{ \tt{ \: \: ^{n}C_{r} = \: ^{n}C_{n - r} \:}}$

$\boxed{ \tt{ \: \: ^{n}C_{0} = \: ^{n}C_{n } = 1\:}}$

$\boxed{ \tt{ \: \: ^{n}C_{1} = \: ^{n}C_{n - 1} = n\:}}$

$\boxed{ \tt{ \: \: ^{n}C_{2} = \: ^{n}C_{n - 2} = \frac{n(n - 1)}{2} \:}}$

$\boxed{ \tt{ \: ^{n}C_{r} = \frac{n}{r} \: ^{n - 1}C_{r - 1} \: }}$

$\boxed{ \tt{ \: ^{n}C_{r} \: + \: ^{n}C_{r - 1} \: = \: ^{n + 1}C_{r} \: }}$

$\boxed{ \tt{ \: \frac{^{n}C_{r}}{^{n}C_{r - 1}} = \frac{n - r + 1}{r} \: }}$