Question

Six persons sitting in a row are given one sweet each from three types of sweets such that no two adjacent person gets same type of sweet. In how many ways can the sweets be distributed among the persons?
A) 36
B) None
C) 20
D) 72

Answer 1

b) none

Six persons sitting in a row are given one sweet each from three types of sweets such that no two adjacent person gets same type of sweet. In how many ways can the sweets be distributed among the persons?

A) 36

B) None

C) 20

D) 72

Answer 2

Answer:

The sweets can be distributed in 20 ways among the six persons.

Combination:

• Combination refers to the selection of objects from a set.
• In combination, the order of selection is not important.
• It is denoted as ${n}_C_{r}$ and the formula is $\frac{n!}{r!(n-r)!}$ where n is the total number of objects and r is the number of chosen objects.
• Example of a combination: picking 2 balls randomly out of 10.

Step-by-step explanation:

Step 1:

Since there are 6 people, the total number of sweets will also be 6.

Therefore, n = 6

There are three types of sweets to be chosen from.

Therefore, r = 3

Step 2:

Using the formula for combination and substituting the above values.

${n}_C_{r} = \frac{n!}{r!(n-r)!}$

${6}_C_{3} = \frac{6!}{3!(6-3)!}$

${6}_C_{3} = \frac{6!}{3!3!}$

${6}_C_{3} = \frac{6*5*4*3!}{3!3!}$

${6}_C_{3} = \frac{6*5*4}{3*2*1}$

${6}_C_{3} = 5*4$

${6}_C_{3} = 20$

Therefore, there are 20 ways to distribute the sweets.

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