If the number of arrangements of 4 alike apples, 5 alike mangoes, 1 banana and 1 orange in which all the apples are together or all the mangoes are together is K, then find the sum of digits in K.

Question

If the number of arrangements of 4 alike apples, 5 alike mangoes, 1 banana and 1 orange in which all the apples are together or all the mangoes are together is K, then find the sum of digits in K. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

No. of ways when Apples are together + no. of ways when mangoes are together - No. of ways when Apples are also and Mangoes are also together (8 !/5 !)+(7 !/4 !)-4 ! ⇒ k=522 ⇒ 9

Q. If the number of arrangements of $4$ alike apples, $5$ alike mangoes, $1$ banana and $1$ orange in which all the apples are together or all the mangoes are together is $K$ , then find the sum of digits in $K$ .

No. of ways when Apples are together $+$ no. of ways when mangoes are together - No. of ways when Apples are also and Mangoes are also together
$\frac{8 !}{5 !} + \frac{7 !}{4 !} - 4!$
$\Rightarrow k = 522 \Rightarrow 9$

Q. If the number of arrangements of 4 alike apples, 5 alike mangoes, 1 banana and 1 orange in which all the apples are together or all the mangoes are together is K, then find the sum of digits in K.

No. of ways when Apples are together + no. of ways when mangoes are together - No. of ways when Apples are also and Mangoes are also together 5!8!​+4!7!​−4! ⇒k=522⇒9

Q. If the number of arrangements of $4$ alike apples, $5$ alike mangoes, $1$ banana and $1$ orange in which all the apples are together or all the mangoes are together is $K$ , then find the sum of digits in $K$ .

No. of ways when Apples are together $+$ no. of ways when mangoes are together - No. of ways when Apples are also and Mangoes are also together
$\frac{8 !}{5 !} + \frac{7 !}{4 !} - 4!$
$\Rightarrow k = 522 \Rightarrow 9$