Answer
Verified
388.2k+ views
Hint: Find the total number of arrangement of flowers. In this question it is given that 3 white flowers and 4 blue flowers are similar so we need to divide the total number of arrangements by 3! And factorial 4!. Use combinations formula \[\dfrac{{n!}}{{p!q!r!}}\]
Complete step-by-step answer:
Given total number of white flowers is 3
Total number of blue flowers is 4
Total number of red flower is 1
We need to find the total number of arrangements in a row such that All of them are taken out one by one and arranged in a row in the order.
The total number of ways of arranging these flowers will be 8!
However, there are 3 white flowers, 4 red flowers and 1 blue flower.
The total number of ways of arranging 3 white flowers will be 3!
The total number of ways of arranging 4 blue flowers will be 4!
Since there is a repetition of 3 and 4, the answer will be:
We have,
Total no. of different arrangements \[\dfrac{{8!}}{{3!4!}}\]
\[ = 8 \times 7 \times 5 = 280\]arrangements
Note:1.the number of arrangement of a total of n objects, out of which ‘p’ are of one type, q of second type are alike, and r of a third kind are same, then such a computation is done by \[\dfrac{{n!}}{{p!q!r!}}\]
2. Number of ways in which n things of which r alike and the rest different can be arranged in a circle distinguishing between clockwise and anticlockwise arrangement, is $\dfrac{{\left( {n - 1} \right)!}}{r}$
Complete step-by-step answer:
Given total number of white flowers is 3
Total number of blue flowers is 4
Total number of red flower is 1
We need to find the total number of arrangements in a row such that All of them are taken out one by one and arranged in a row in the order.
The total number of ways of arranging these flowers will be 8!
However, there are 3 white flowers, 4 red flowers and 1 blue flower.
The total number of ways of arranging 3 white flowers will be 3!
The total number of ways of arranging 4 blue flowers will be 4!
Since there is a repetition of 3 and 4, the answer will be:
We have,
Total no. of different arrangements \[\dfrac{{8!}}{{3!4!}}\]
\[ = 8 \times 7 \times 5 = 280\]arrangements
Note:1.the number of arrangement of a total of n objects, out of which ‘p’ are of one type, q of second type are alike, and r of a third kind are same, then such a computation is done by \[\dfrac{{n!}}{{p!q!r!}}\]
2. Number of ways in which n things of which r alike and the rest different can be arranged in a circle distinguishing between clockwise and anticlockwise arrangement, is $\dfrac{{\left( {n - 1} \right)!}}{r}$
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE