There are three boys and three girls at a party. in how many ways can they be seated in a row if they must sit alternating boys
1 answer:
The number of permutations of the three girls is 3P3 = 6. Similarly the number of permutations of the boys is 6. Each permutation of girls can be taken with each permutation of boys. Additionally each arrangement from left to righr can have a girl first or a boy first.
Total number of ways is given by:
Total number of ways is given by:
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Answer:
Step-by-step explanation:
We know: the denominator must be different than 0.
Therefore
<em>add 8 to both sides</em>
<em>divide both sides by 2</em>
Answer with Step-by-step explanation:
Permutation : It is an arrangement of r elements out of n elements.
Combination : it is a selection of r element out of n elements .
Suppose we have a set
S={1,2,3}
If two elements are taken at a time then
Using permutation formula
Total number of outcomes=
Total number of outcomes=
Total number of outcomes=3!=
Using combination formula
Total number of outcomes=
Total number of outcomes=
Hence, total number of outcomes=3
Total number of outcomes determined by permutation have more outcomes.
Because permutation is an arrangement of elements therefore, it consider order of arrangement of element but combination is a selection of elements it does no consider order of elements
Arrangements of two elements out of 3 elements
{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}
By using combination if two elements taken at a time then combination
{1,2},{2,3},{1,3}