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The value of ⁵⁰C₄ + $not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscript$ is -

⁵⁵C₄
⁵⁵C₃
⁵⁶C₃
⁵⁶C₄

hint Hint:

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Here we have to find the value of 50C4 + $not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscript$ .

The correct answer is: ⁵⁶C₄

A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.
$P presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial end fraction$
A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.
$C presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial cross times r factorial end fraction$
Here we have given:
$C presuperscript 50 subscript 4 plus begin inline style sum from r equals 1 to 6 of end style space C presuperscript 56 minus r end presuperscript subscript 3 S o l v i n g space t h i s comma space w e space g e t colon C presuperscript 50 subscript 4 plus C presuperscript 50 subscript 3 plus C presuperscript 51 subscript 3 plus C presuperscript 52 subscript 3 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3 N o w space u s n i n g space t h e space f o r m u l a colon C presuperscript n subscript i plus C presuperscript n subscript i minus 1 end subscript equals C presuperscript n plus 1 end presuperscript subscript i A p p l y i n g space t h i s comma space w e space g e t colon C presuperscript 51 subscript 4 plus C presuperscript 51 subscript 3 plus C presuperscript 52 subscript 3 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3 A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon C presuperscript 52 subscript 4 plus C presuperscript 52 subscript 3 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3 A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon C presuperscript 53 subscript 4 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3 A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon C presuperscript 54 subscript 4 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3 A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon C presuperscript 55 subscript 4 plus C presuperscript 55 subscript 3 A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon C presuperscript 56 subscript 4$

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is $C presuperscript 56 subscript 4$ .

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The value of 50C4 + is -

55C4 55C3 56C3 56C4

The correct answer is: 56C4

A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.Here we have given:

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The value of ⁵⁰C₄ + $not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscript$ is -

⁵⁵C₄
⁵⁵C₃
⁵⁶C₃
⁵⁶C₄

The correct answer is: ⁵⁶C₄

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

An intense stream of water of cross-sectional area $A$ strikes a wall at an angle $theta$ with the normal to the wall and returns back elastically. If the density of water is $rho$ and its velocity is $v$ ,then the force exerted in the wall will be

An intense stream of water of cross-sectional area $A$ strikes a wall at an angle $theta$ with the normal to the wall and returns back elastically. If the density of water is $rho$ and its velocity is $v$ ,then the force exerted in the wall will be

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line $O A$ will

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line $O A$ will

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than $C H subscript 2 end subscript C O O to the power of minus end exponent$

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than $C H subscript 2 end subscript C O O to the power of minus end exponent$